LMFDB - Embedded newform 38.4.c.c.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(7,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 $ x^6 - x^5 + 64x^4 + 33x^3 + 3984x^2 - 945x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.2
Root			$0.118706 - 0.205606i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.4.c.c.11.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-0.881294 - 1.52645i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(10.3546 + 17.9347i) q^{5} +(1.76259 - 3.05289i) q^{6} +8.76259 q^{7} -8.00000 q^{8} +(11.9466 - 20.6922i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-0.881294 - 1.52645i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(10.3546 + 17.9347i) q^{5} +(1.76259 - 3.05289i) q^{6} +8.76259 q^{7} -8.00000 q^{8} +(11.9466 - 20.6922i) q^{9} +(-20.7092 + 35.8694i) q^{10} -62.1780 q^{11} +7.05035 q^{12} +(32.2611 - 55.8778i) q^{13} +(8.76259 + 15.1772i) q^{14} +(18.2509 - 31.6115i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(23.2077 + 40.1970i) q^{17} +47.7866 q^{18} +(17.3798 - 80.9750i) q^{19} -82.8369 q^{20} +(-7.72241 - 13.3756i) q^{21} +(-62.1780 - 107.696i) q^{22} +(18.6424 - 32.2895i) q^{23} +(7.05035 + 12.2116i) q^{24} +(-151.936 + 263.161i) q^{25} +129.044 q^{26} -89.7038 q^{27} +(-17.5252 + 30.3545i) q^{28} +(33.2119 - 57.5247i) q^{29} +73.0036 q^{30} +112.370 q^{31} +(16.0000 - 27.7128i) q^{32} +(54.7971 + 94.9114i) q^{33} +(-46.4155 + 80.3939i) q^{34} +(90.7332 + 157.155i) q^{35} +(47.7866 + 82.7688i) q^{36} -189.018 q^{37} +(157.633 - 50.8723i) q^{38} -113.726 q^{39} +(-82.8369 - 143.478i) q^{40} +(120.005 + 207.854i) q^{41} +(15.4448 - 26.7512i) q^{42} +(-84.1370 - 145.730i) q^{43} +(124.356 - 215.391i) q^{44} +494.812 q^{45} +74.5695 q^{46} +(-93.9241 + 162.681i) q^{47} +(-14.1007 + 24.4231i) q^{48} -266.217 q^{49} -607.744 q^{50} +(40.9056 - 70.8506i) q^{51} +(129.044 + 223.511i) q^{52} +(56.5285 - 97.9102i) q^{53} +(-89.7038 - 155.372i) q^{54} +(-643.830 - 1115.15i) q^{55} -70.1007 q^{56} +(-138.921 + 44.8334i) q^{57} +132.848 q^{58} +(-92.9940 - 161.070i) q^{59} +(73.0036 + 126.446i) q^{60} +(-154.322 + 267.293i) q^{61} +(112.370 + 194.631i) q^{62} +(104.684 - 181.317i) q^{63} +64.0000 q^{64} +1336.20 q^{65} +(-109.594 + 189.823i) q^{66} +(-19.7279 + 34.1697i) q^{67} -185.662 q^{68} -65.7176 q^{69} +(-181.466 + 314.309i) q^{70} +(175.101 + 303.284i) q^{71} +(-95.5731 + 165.538i) q^{72} +(4.80280 + 8.31870i) q^{73} +(-189.018 - 327.389i) q^{74} +535.601 q^{75} +(245.746 + 222.155i) q^{76} -544.840 q^{77} +(-113.726 - 196.979i) q^{78} +(588.269 + 1018.91i) q^{79} +(165.674 - 286.956i) q^{80} +(-243.504 - 421.761i) q^{81} +(-240.010 + 415.709i) q^{82} -257.980 q^{83} +61.7793 q^{84} +(-480.614 + 832.448i) q^{85} +(168.274 - 291.459i) q^{86} -117.078 q^{87} +497.424 q^{88} +(66.8743 - 115.830i) q^{89} +(494.812 + 857.039i) q^{90} +(282.691 - 489.634i) q^{91} +(74.5695 + 129.158i) q^{92} +(-99.0313 - 171.527i) q^{93} -375.696 q^{94} +(1632.22 - 526.763i) q^{95} -56.4028 q^{96} +(-598.387 - 1036.44i) q^{97} +(-266.217 - 461.101i) q^{98} +(-742.819 + 1286.60i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9	\( 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9} + 2 q^{10} + 8 q^{11} + 40 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} - 48 q^{16} - 51 q^{17} - 216 q^{18} + 40 q^{19} + 8 q^{20} - 170 q^{21} + 8 q^{22} + 47 q^{23} + 40 q^{24} - 338 q^{25} + 516 q^{26} + 718 q^{27} - 104 q^{28} - 125 q^{29} - 308 q^{30} - 100 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} - 84 q^{35} - 216 q^{36} - 376 q^{37} + 322 q^{38} - 1546 q^{39} + 8 q^{40} + 475 q^{41} + 340 q^{42} - 73 q^{43} - 16 q^{44} + 3188 q^{45} + 188 q^{46} - 241 q^{47} - 80 q^{48} - 1354 q^{49} - 1352 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} + 718 q^{54} - 1838 q^{55} - 416 q^{56} + 1755 q^{57} - 500 q^{58} - 1065 q^{59} - 308 q^{60} - 981 q^{61} - 100 q^{62} - 872 q^{63} + 384 q^{64} + 586 q^{65} - 548 q^{66} + 877 q^{67} + 408 q^{68} - 1526 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} + 667 q^{73} - 376 q^{74} + 4584 q^{75} + 484 q^{76} - 492 q^{77} - 1546 q^{78} + 1671 q^{79} - 16 q^{80} - 1287 q^{81} - 950 q^{82} + 1176 q^{83} + 1360 q^{84} - 1929 q^{85} + 146 q^{86} - 6430 q^{87} - 64 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} + 188 q^{92} - 3138 q^{93} - 964 q^{94} + 4489 q^{95} - 320 q^{96} - 985 q^{97} - 1354 q^{98} - 3184 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9 + 2 * q^10 + 8 * q^11 + 40 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 - 48 * q^16 - 51 * q^17 - 216 * q^18 + 40 * q^19 + 8 * q^20 - 170 * q^21 + 8 * q^22 + 47 * q^23 + 40 * q^24 - 338 * q^25 + 516 * q^26 + 718 * q^27 - 104 * q^28 - 125 * q^29 - 308 * q^30 - 100 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 - 84 * q^35 - 216 * q^36 - 376 * q^37 + 322 * q^38 - 1546 * q^39 + 8 * q^40 + 475 * q^41 + 340 * q^42 - 73 * q^43 - 16 * q^44 + 3188 * q^45 + 188 * q^46 - 241 * q^47 - 80 * q^48 - 1354 * q^49 - 1352 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 + 718 * q^54 - 1838 * q^55 - 416 * q^56 + 1755 * q^57 - 500 * q^58 - 1065 * q^59 - 308 * q^60 - 981 * q^61 - 100 * q^62 - 872 * q^63 + 384 * q^64 + 586 * q^65 - 548 * q^66 + 877 * q^67 + 408 * q^68 - 1526 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 + 667 * q^73 - 376 * q^74 + 4584 * q^75 + 484 * q^76 - 492 * q^77 - 1546 * q^78 + 1671 * q^79 - 16 * q^80 - 1287 * q^81 - 950 * q^82 + 1176 * q^83 + 1360 * q^84 - 1929 * q^85 + 146 * q^86 - 6430 * q^87 - 64 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 + 188 * q^92 - 3138 * q^93 - 964 * q^94 + 4489 * q^95 - 320 * q^96 - 985 * q^97 - 1354 * q^98 - 3184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	−0.881294	−	1.52645i	−0.169605	−	0.293765i	0.768676	−	0.639638i	$-0.220916\pi$
$3$	−0.881294	−	1.52645i	−0.169605	−	0.293765i	−0.938281	+	0.345874i	$0.887583\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	10.3546	+	17.9347i	0.926145	+	1.60413i	0.789709	+	0.613481i	$0.210231\pi$
$5$	10.3546	+	17.9347i	0.926145	+	1.60413i	0.136436	+	0.990649i	$0.456435\pi$
$6$	1.76259	−	3.05289i	0.119929	−	0.207723i
$7$	8.76259			0.473135			0.236568	−	0.971615i	$-0.423978\pi$
$7$	8.76259			0.473135			0.236568	+	0.971615i	$0.423978\pi$
$8$	−8.00000			−0.353553
$9$	11.9466	−	20.6922i	0.442468	−	0.766378i
$10$	−20.7092	+	35.8694i	−0.654883	+	1.13429i
$11$	−62.1780			−1.70431			−0.852154	−	0.523291i	$-0.824704\pi$
$11$	−62.1780			−1.70431			−0.852154	+	0.523291i	$0.824704\pi$
$12$	7.05035			0.169605
$13$	32.2611	−	55.8778i	0.688278	−	1.19213i	−0.284117	−	0.958790i	$-0.591700\pi$
$13$	32.2611	−	55.8778i	0.688278	−	1.19213i	0.972395	−	0.233343i	$-0.0749664\pi$
$14$	8.76259	+	15.1772i	0.167279	+	0.289735i
$15$	18.2509	−	31.6115i	0.314158	−	0.544137i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	23.2077	+	40.1970i	0.331100	+	0.573482i	0.982728	−	0.185057i	$-0.0592469\pi$
$17$	23.2077	+	40.1970i	0.331100	+	0.573482i	−0.651628	+	0.758539i	$0.725914\pi$
$18$	47.7866			0.625745
$19$	17.3798	−	80.9750i	0.209852	−	0.977733i
$19$	17.3798	−	80.9750i	0.209852	−	0.977733i
$20$	−82.8369			−0.926145
$21$	−7.72241	−	13.3756i	−0.0802461	−	0.138990i
$22$	−62.1780	−	107.696i	−0.602564	−	1.04367i
$23$	18.6424	−	32.2895i	0.169009	−	0.292732i	−0.769063	−	0.639173i	$-0.779277\pi$
$23$	18.6424	−	32.2895i	0.169009	−	0.292732i	0.938072	+	0.346441i	$0.112610\pi$
$24$	7.05035	+	12.2116i	0.0599644	+	0.103861i
$25$	−151.936	+	263.161i	−1.21549	+	2.10529i
$26$	129.044			0.973372
$27$	−89.7038			−0.639389
$28$	−17.5252	+	30.3545i	−0.118284	+	0.204874i
$29$	33.2119	−	57.5247i	0.212665	−	0.368347i	−0.739883	−	0.672736i	$-0.765119\pi$
$29$	33.2119	−	57.5247i	0.212665	−	0.368347i	0.952548	+	0.304389i	$0.0984523\pi$
$30$	73.0036			0.444286
$31$	112.370			0.651043			0.325521	−	0.945535i	$-0.394460\pi$
$31$	112.370			0.651043			0.325521	+	0.945535i	$0.394460\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	54.7971	+	94.9114i	0.289059	+	0.500665i
$34$	−46.4155	+	80.3939i	−0.234123	+	0.405513i
$35$	90.7332	+	157.155i	0.438192	+	0.758970i
$36$	47.7866	+	82.7688i	0.221234	+	0.383189i
$37$	−189.018			−0.839848			−0.419924	−	0.907559i	$-0.637943\pi$
$37$	−189.018			−0.839848			−0.419924	+	0.907559i	$0.637943\pi$
$38$	157.633	−	50.8723i	0.672931	−	0.217173i
$39$	−113.726			−0.466942
$40$	−82.8369	−	143.478i	−0.327442	−	0.567146i
$41$	120.005	+	207.854i	0.457112	+	0.791742i	0.998807	−	0.0488336i	$-0.0155504\pi$
$41$	120.005	+	207.854i	0.457112	+	0.791742i	−0.541695	+	0.840575i	$0.682217\pi$
$42$	15.4448	−	26.7512i	0.0567426	−	0.0982810i
$43$	−84.1370	−	145.730i	−0.298390	−	0.516827i	0.677378	−	0.735635i	$-0.263116\pi$
$43$	−84.1370	−	145.730i	−0.298390	−	0.516827i	−0.975768	+	0.218809i	$0.929783\pi$
$44$	124.356	−	215.391i	0.426077	−	0.737987i
$45$	494.812			1.63916
$46$	74.5695			0.239015
$47$	−93.9241	+	162.681i	−0.291494	+	0.504883i	−0.974163	−	0.225845i	$-0.927486\pi$
$47$	−93.9241	+	162.681i	−0.291494	+	0.504883i	0.682669	+	0.730728i	$0.260819\pi$
$48$	−14.1007	+	24.4231i	−0.0424013	+	0.0734411i
$49$	−266.217			−0.776143
$50$	−607.744			−1.71896
$51$	40.9056	−	70.8506i	0.112312	−	0.194531i
$52$	129.044	+	223.511i	0.344139	+	0.596066i
$53$	56.5285	−	97.9102i	0.146505	−	0.253755i	−0.783428	−	0.621482i	$-0.786531\pi$
$53$	56.5285	−	97.9102i	0.146505	−	0.253755i	0.929934	+	0.367728i	$0.119864\pi$
$54$	−89.7038	−	155.372i	−0.226058	−	0.391544i
$55$	−643.830	−	1115.15i	−1.57844	−	2.73393i
$56$	−70.1007			−0.167279
$57$	−138.921	+	44.8334i	−0.322815	+	0.104181i
$58$	132.848			0.300754
$59$	−92.9940	−	161.070i	−0.205200	−	0.355417i	0.744997	−	0.667068i	$-0.232451\pi$
$59$	−92.9940	−	161.070i	−0.205200	−	0.355417i	−0.950196	+	0.311652i	$0.899118\pi$
$60$	73.0036	+	126.446i	0.157079	+	0.272069i
$61$	−154.322	+	267.293i	−0.323916	+	0.561038i	−0.981292	−	0.192524i	$-0.938333\pi$
$61$	−154.322	+	267.293i	−0.323916	+	0.561038i	0.657377	+	0.753562i	$0.271666\pi$
$62$	112.370	+	194.631i	0.230178	+	0.398681i
$63$	104.684	−	181.317i	0.209347	−	0.362600i
$64$	64.0000			0.125000
$65$	1336.20			2.54978
$66$	−109.594	+	189.823i	−0.204396	+	0.354024i
$67$	−19.7279	+	34.1697i	−0.0359723	+	0.0623058i	−0.883451	−	0.468523i	$-0.844786\pi$
$67$	−19.7279	+	34.1697i	−0.0359723	+	0.0623058i	0.847479	+	0.530829i	$0.178119\pi$
$68$	−185.662			−0.331100
$69$	−65.7176			−0.114659
$70$	−181.466	+	314.309i	−0.309848	+	0.536673i
$71$	175.101	+	303.284i	0.292686	+	0.506946i	0.974444	−	0.224631i	$-0.0721177\pi$
$71$	175.101	+	303.284i	0.292686	+	0.506946i	−0.681758	+	0.731578i	$0.738784\pi$
$72$	−95.5731	+	165.538i	−0.156436	+	0.270955i
$73$	4.80280	+	8.31870i	0.00770035	+	0.0133374i	0.869850	−	0.493316i	$-0.164216\pi$
$73$	4.80280	+	8.31870i	0.00770035	+	0.0133374i	−0.862150	+	0.506654i	$0.830882\pi$
$74$	−189.018	−	327.389i	−0.296931	−	0.514300i
$75$	535.601			0.824612
$76$	245.746	+	222.155i	0.370908	+	0.335302i
$77$	−544.840			−0.806368
$78$	−113.726	−	196.979i	−0.165089	−	0.285942i
$79$	588.269	+	1018.91i	0.837791	+	1.45110i	0.891738	+	0.452552i	$0.149486\pi$
$79$	588.269	+	1018.91i	0.837791	+	1.45110i	−0.0539471	+	0.998544i	$0.517180\pi$
$80$	165.674	−	286.956i	0.231536	−	0.401033i
$81$	−243.504	−	421.761i	−0.334025	−	0.578548i
$82$	−240.010	+	415.709i	−0.323227	+	0.559846i
$83$	−257.980			−0.341168			−0.170584	−	0.985343i	$-0.554565\pi$
$83$	−257.980			−0.341168			−0.170584	+	0.985343i	$0.554565\pi$
$84$	61.7793			0.0802461
$85$	−480.614	+	832.448i	−0.613293	+	1.06226i
$86$	168.274	−	291.459i	0.210994	−	0.365452i
$87$	−117.078			−0.144276
$88$	497.424			0.602564
$89$	66.8743	−	115.830i	0.0796479	−	0.137954i	−0.823450	−	0.567389i	$-0.807954\pi$
$89$	66.8743	−	115.830i	0.0796479	−	0.137954i	0.903098	+	0.429434i	$0.141287\pi$
$90$	494.812	+	857.039i	0.579530	+	1.00378i
$91$	282.691	−	489.634i	0.325649	−	0.564040i
$92$	74.5695	+	129.158i	0.0845044	+	0.146366i
$93$	−99.0313	−	171.527i	−0.110420	−	0.191253i
$94$	−375.696			−0.412235
$95$	1632.22	−	526.763i	1.76276	−	0.568892i
$96$	−56.4028			−0.0599644
$97$	−598.387	−	1036.44i	−0.626361	−	1.08489i	−0.988276	−	0.152678i	$-0.951210\pi$
$97$	−598.387	−	1036.44i	−0.626361	−	1.08489i	0.361915	−	0.932211i	$-0.382123\pi$
$98$	−266.217	−	461.101i	−0.274408	−	0.475289i
$99$	−742.819	+	1286.60i	−0.754102	+	1.30614i
$100$	−607.744	−	1052.64i	−0.607744	−	1.05264i
$101$	−434.472	+	752.527i	−0.428035	+	0.741378i	−0.996698	−	0.0811919i	$-0.974127\pi$
$101$	−434.472	+	752.527i	−0.428035	+	0.741378i	0.568663	+	0.822570i	$0.307461\pi$
$102$	163.623			0.158834
$103$	−1491.56			−1.42687			−0.713437	−	0.700720i	$-0.752862\pi$
$103$	−1491.56			−1.42687			−0.713437	+	0.700720i	$0.752862\pi$
$104$	−258.089	+	447.023i	−0.243343	+	0.421482i
$105$	159.925	−	276.999i	0.148639	−	0.257450i
$106$	226.114			0.207190
$107$	−1610.18			−1.45478			−0.727392	−	0.686222i	$-0.759268\pi$
$107$	−1610.18			−1.45478			−0.727392	+	0.686222i	$0.759268\pi$
$108$	179.408	−	310.743i	0.159847	−	0.276864i
$109$	25.5111	+	44.1865i	0.0224176	+	0.0388284i	0.877017	−	0.480460i	$-0.159530\pi$
$109$	25.5111	+	44.1865i	0.0224176	+	0.0388284i	−0.854599	+	0.519289i	$0.826197\pi$
$110$	1287.66	−	2230.29i	1.11612	−	1.93318i
$111$	166.580	+	288.526i	0.142442	+	0.246717i
$112$	−70.1007	−	121.418i	−0.0591419	−	0.102437i
$113$	1789.55			1.48979			0.744895	−	0.667181i	$-0.232499\pi$
$113$	1789.55			1.48979			0.744895	+	0.667181i	$0.232499\pi$
$114$	−216.574	−	195.784i	−0.177930	−	0.160850i
$115$	772.139			0.626107
$116$	132.848	+	230.099i	0.106333	+	0.184173i
$117$	−770.823	−	1335.11i	−0.609082	−	1.05496i
$118$	185.988	−	322.141i	0.145098	−	0.251317i
$119$	203.360	+	352.229i	0.156655	+	0.271335i
$120$	−146.007	+	252.892i	−0.111072	+	0.192381i
$121$	2535.11			1.90466
$122$	−617.286			−0.458086
$123$	211.519	−	366.362i	0.155057	−	0.268567i
$124$	−224.741	+	389.263i	−0.162761	+	0.281910i
$125$	−3704.31			−2.65059
$126$	418.734			0.296062
$127$	−138.888	+	240.560i	−0.0970416	+	0.168081i	−0.910459	−	0.413600i	$-0.864271\pi$
$127$	−138.888	+	240.560i	−0.0970416	+	0.168081i	0.813417	+	0.581681i	$0.197605\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−148.299	+	256.861i	−0.101217	+	0.175313i
$130$	1336.20	+	2314.37i	0.901484	+	1.56142i
$131$	911.342	+	1578.49i	0.607819	+	1.05277i	0.991599	+	0.129349i	$0.0412887\pi$
$131$	911.342	+	1578.49i	0.607819	+	1.05277i	−0.383780	+	0.923424i	$0.625378\pi$
$132$	−438.377			−0.289059
$133$	152.292	−	709.550i	0.0992886	−	0.462600i
$134$	−78.9115			−0.0508725
$135$	−928.849	−	1608.81i	−0.592167	−	1.02566i
$136$	−185.662	−	321.576i	−0.117062	−	0.202757i
$137$	−330.481	+	572.411i	−0.206094	+	0.356966i	−0.950481	−	0.310783i	$-0.899409\pi$
$137$	−330.481	+	572.411i	−0.206094	+	0.356966i	0.744386	+	0.667749i	$0.232742\pi$
$138$	−65.7176	−	113.826i	−0.0405381	−	0.0702140i
$139$	622.975	−	1079.02i	0.380144	−	0.658429i	−0.610938	−	0.791678i	$-0.709208\pi$
$139$	622.975	−	1079.02i	0.380144	−	0.658429i	0.991083	+	0.133249i	$0.0425410\pi$
$140$	−725.866			−0.438192
$141$	331.099			0.197756
$142$	−350.202	+	606.568i	−0.206960	+	0.358465i
$143$	−2005.93	+	3474.37i	−1.17304	+	2.03176i
$144$	−382.293			−0.221234
$145$	1375.59			0.787835
$146$	−9.60561	+	16.6374i	−0.00544497	+	0.00943096i
$147$	234.615	+	406.366i	0.131638	+	0.228003i
$148$	378.036	−	654.777i	0.209962	−	0.363665i
$149$	−1136.01	−	1967.62i	−0.624599	−	1.08184i	−0.988618	−	0.150446i	$-0.951929\pi$
$149$	−1136.01	−	1967.62i	−0.624599	−	1.08184i	0.364019	−	0.931392i	$-0.381404\pi$
$150$	535.601	+	927.689i	0.291544	+	0.504970i
$151$	3637.77			1.96051			0.980256	−	0.197734i	$-0.0633581\pi$
$151$	3637.77			1.96051			0.980256	+	0.197734i	$0.0633581\pi$
$152$	−139.038	+	647.800i	−0.0741941	+	0.345681i
$153$	1109.02			0.586005
$154$	−544.840	−	943.691i	−0.285094	−	0.493798i
$155$	1163.55	+	2015.33i	0.602960	+	1.04436i
$156$	227.452	−	393.958i	0.116735	−	0.202192i
$157$	225.885	+	391.244i	0.114825	+	0.198883i	0.917710	−	0.397251i	$-0.130036\pi$
$157$	225.885	+	391.244i	0.114825	+	0.198883i	−0.802885	+	0.596135i	$0.796702\pi$
$158$	−1176.54	+	2037.82i	−0.592408	+	1.02608i
$159$	−199.273			−0.0993922
$160$	662.695			0.327442
$161$	163.355	−	282.940i	0.0799641	−	0.138502i
$162$	487.008	−	843.522i	0.236191	−	0.409095i
$163$	215.631			0.103617			0.0518084	−	0.998657i	$-0.483502\pi$
$163$	215.631			0.103617			0.0518084	+	0.998657i	$0.483502\pi$
$164$	−960.039			−0.457112
$165$	−1134.81	+	1965.54i	−0.535421	+	0.927377i
$166$	−257.980	−	446.834i	−0.120621	−	0.208922i
$167$	1660.74	−	2876.49i	0.769533	−	1.33287i	−0.168283	−	0.985739i	$-0.553822\pi$
$167$	1660.74	−	2876.49i	0.769533	−	1.33287i	0.937816	−	0.347132i	$-0.112844\pi$
$168$	61.7793	+	107.005i	0.0283713	+	0.0491405i
$169$	−983.055	−	1702.70i	−0.447453	−	0.775012i
$170$	−1922.46			−0.867328
$171$	−1467.92	−	1327.00i	−0.656460	−	0.593442i
$172$	673.096			0.298390
$173$	−736.228	−	1275.19i	−0.323552	−	0.560408i	0.657667	−	0.753309i	$-0.271544\pi$
$173$	−736.228	−	1275.19i	−0.323552	−	0.560408i	−0.981218	+	0.192901i	$0.938210\pi$
$174$	−117.078	−	202.784i	−0.0510094	−	0.0883509i
$175$	−1331.35	+	2305.97i	−0.575091	+	0.996086i
$176$	497.424	+	861.564i	0.213038	+	0.368993i
$177$	−163.910	+	283.901i	−0.0696058	+	0.120561i
$178$	267.497			0.112639
$179$	3573.98			1.49236			0.746179	−	0.665745i	$-0.231886\pi$
$179$	3573.98			1.49236			0.746179	+	0.665745i	$0.231886\pi$
$180$	−989.623	+	1714.08i	−0.409790	+	0.709777i
$181$	1471.86	−	2549.34i	0.604436	−	1.04691i	−0.387705	−	0.921784i	$-0.626732\pi$
$181$	1471.86	−	2549.34i	0.604436	−	1.04691i	0.992140	−	0.125130i	$-0.0399347\pi$
$182$	1130.76			0.460537
$183$	544.011			0.219751
$184$	−149.139	+	258.316i	−0.0597537	+	0.103496i
$185$	−1957.21	−	3389.98i	−0.777821	−	1.34722i
$186$	198.063	−	343.055i	0.0780788	−	0.135236i
$187$	−1443.01	−	2499.37i	−0.564296	−	0.977390i
$188$	−375.696	−	650.725i	−0.145747	−	0.252442i
$189$	−786.038			−0.302518
$190$	2544.60	+	2300.33i	0.971605	+	0.878335i
$191$	−700.359			−0.265321			−0.132660	−	0.991162i	$-0.542352\pi$
$191$	−700.359			−0.265321			−0.132660	+	0.991162i	$0.542352\pi$
$192$	−56.4028	−	97.6925i	−0.0212006	−	0.0367206i
$193$	29.9508	+	51.8763i	0.0111705	+	0.0193478i	0.871557	−	0.490295i	$-0.163111\pi$
$193$	29.9508	+	51.8763i	0.0111705	+	0.0193478i	−0.860386	+	0.509643i	$0.829778\pi$
$194$	1196.77	−	2072.87i	0.442904	−	0.767132i
$195$	−1177.59	−	2039.64i	−0.432456	−	0.749035i
$196$	532.434	−	922.203i	0.194036	−	0.336080i
$197$	−374.382			−0.135399			−0.0676994	−	0.997706i	$-0.521566\pi$
$197$	−374.382			−0.135399			−0.0676994	+	0.997706i	$0.521566\pi$
$198$	−2971.28			−1.06646
$199$	−2301.88	+	3986.98i	−0.819981	+	1.42025i	0.0857147	+	0.996320i	$0.472683\pi$
$199$	−2301.88	+	3986.98i	−0.819981	+	1.42025i	−0.905696	+	0.423929i	$0.860651\pi$
$200$	1215.49	−	2105.29i	0.429740	−	0.744332i
$201$	69.5442			0.0244043
$202$	−1737.89			−0.605333
$203$	291.022	−	504.065i	0.100619	−	0.174278i
$204$	163.623	+	283.403i	0.0561562	+	0.0972654i
$205$	−2485.21	+	4304.51i	−0.846705	+	1.46654i
$206$	−1491.56	−	2583.46i	−0.504476	−	0.873778i
$207$	−445.428	−	771.503i	−0.149562	−	0.259049i
$208$	−1032.35			−0.344139
$209$	−1080.64	+	5034.86i	−0.357653	+	1.66636i
$210$	639.701			0.210207
$211$	1478.36	+	2560.60i	0.482344	+	0.835444i	0.999795	−	0.0202687i	$-0.00645218\pi$
$211$	1478.36	+	2560.60i	0.482344	+	0.835444i	−0.517451	+	0.855713i	$0.673119\pi$
$212$	226.114	+	391.641i	0.0732527	+	0.126877i
$213$	308.631	−	534.564i	0.0992819	−	0.171961i
$214$	−1610.18	−	2788.91i	−0.514344	−	0.890870i
$215$	1742.41	−	3017.95i	0.552705	−	0.957313i
$216$	717.631			0.226058
$217$	984.655			0.308031
$218$	−51.0222	+	88.3730i	−0.0158516	+	0.0274558i
$219$	8.46536	−	14.6624i	0.00261204	−	0.00452418i
$220$	5150.64			1.57844
$221$	2994.83			0.911555
$222$	−333.161	+	577.051i	−0.100722	+	0.174456i
$223$	−265.320	−	459.548i	−0.0796733	−	0.137998i	0.823436	−	0.567410i	$-0.192054\pi$
$223$	−265.320	−	459.548i	−0.0796733	−	0.137998i	−0.903109	+	0.429411i	$0.858721\pi$
$224$	140.201	−	242.836i	0.0418196	−	0.0724337i
$225$	3630.25	+	6287.78i	1.07563	+	1.86305i
$226$	1789.55	+	3099.58i	0.526720	+	0.912307i
$227$	−3479.72			−1.01743			−0.508716	−	0.860934i	$-0.669880\pi$
$227$	−3479.72			−1.01743			−0.508716	+	0.860934i	$0.669880\pi$
$228$	122.534	−	570.902i	0.0355920	−	0.165828i
$229$	3566.48			1.02917			0.514584	−	0.857440i	$-0.327946\pi$
$229$	3566.48			1.02917			0.514584	+	0.857440i	$0.327946\pi$
$230$	772.139	+	1337.38i	0.221362	+	0.383411i
$231$	480.164	+	831.669i	0.136764	+	0.236882i
$232$	−265.695	+	460.197i	−0.0751885	+	0.130230i
$233$	2995.60	+	5188.53i	0.842267	+	1.45885i	0.887974	+	0.459894i	$0.152113\pi$
$233$	2995.60	+	5188.53i	0.842267	+	1.45885i	−0.0457068	+	0.998955i	$0.514554\pi$
$234$	1541.65	−	2670.21i	0.430686	−	0.745971i
$235$	−3890.19			−1.07986
$236$	743.952			0.205200
$237$	1036.88	−	1795.92i	0.284187	−	0.492226i
$238$	−406.719	+	704.459i	−0.110772	+	0.191863i
$239$	−606.478			−0.164141			−0.0820707	−	0.996627i	$-0.526153\pi$
$239$	−606.478			−0.164141			−0.0820707	+	0.996627i	$0.526153\pi$
$240$	−584.029			−0.157079
$241$	1722.58	−	2983.60i	0.460421	−	0.797472i	−0.538561	−	0.842586i	$-0.681032\pi$
$241$	1722.58	−	2983.60i	0.460421	−	0.797472i	0.998982	+	0.0451143i	$0.0143652\pi$
$242$	2535.11	+	4390.94i	0.673401	+	1.16636i
$243$	−1640.20	+	2840.91i	−0.432999	+	0.749977i
$244$	−617.286	−	1069.17i	−0.161958	−	0.280519i
$245$	−2756.58	−	4774.53i	−0.718821	−	1.24503i
$246$	846.076			0.219284
$247$	−3964.01	−	3583.48i	−1.02115	−	0.923124i
$248$	−898.963			−0.230178
$249$	227.356	+	393.792i	0.0578638	+	0.100223i
$250$	−3704.31	−	6416.05i	−0.937124	−	1.62315i
$251$	−902.687	+	1563.50i	−0.227000	+	0.393176i	−0.956918	−	0.290359i	$-0.906225\pi$
$251$	−902.687	+	1563.50i	−0.227000	+	0.393176i	0.729917	+	0.683535i	$0.239559\pi$
$252$	418.734	+	725.269i	0.104674	+	0.181300i
$253$	−1159.15	+	2007.70i	−0.288043	+	0.498905i
$254$	−555.551			−0.137238
$255$	1694.25			0.416070
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1118.48	+	1937.27i	−0.271475	+	0.470208i	−0.969240	−	0.246119i	$-0.920845\pi$
$257$	−1118.48	+	1937.27i	−0.271475	+	0.470208i	0.697765	+	0.716327i	$0.254178\pi$
$258$	−593.195			−0.143142
$259$	−1656.29			−0.397362
$260$	−2672.41	+	4628.75i	−0.637445	+	1.10409i
$261$	−793.541	−	1374.45i	−0.188195	−	0.325964i
$262$	−1822.68	+	3156.98i	−0.429793	+	0.744423i
$263$	−416.129	−	720.757i	−0.0975651	−	0.168988i	0.813111	−	0.582108i	$-0.197772\pi$
$263$	−416.129	−	720.757i	−0.0975651	−	0.168988i	−0.910676	+	0.413121i	$0.864439\pi$
$264$	−438.377	−	759.291i	−0.102198	−	0.177012i
$265$	2341.32			0.542741
$266$	1381.27	−	445.773i	0.318387	−	0.102752i
$267$	−235.743			−0.0540347
$268$	−78.9115	−	136.679i	−0.0179861	−	0.0311529i
$269$	1741.94	+	3017.13i	0.394826	+	0.683858i	0.993079	−	0.117449i	$-0.0374716\pi$
$269$	1741.94	+	3017.13i	0.394826	+	0.683858i	−0.598253	+	0.801307i	$0.704138\pi$
$270$	1857.70	−	3217.63i	0.418725	−	0.725254i
$271$	−894.554	−	1549.41i	−0.200518	−	0.347307i	0.748178	−	0.663498i	$-0.230929\pi$
$271$	−894.554	−	1549.41i	−0.200518	−	0.347307i	−0.948695	+	0.316192i	$0.897596\pi$
$272$	371.324	−	643.151i	0.0827750	−	0.143371i
$273$	−996.533			−0.220927
$274$	−1321.93			−0.291462
$275$	9447.09	−	16362.8i	2.07157	−	3.58806i
$276$	131.435	−	227.653i	0.0286648	−	0.0496488i
$277$	−5548.66			−1.20356			−0.601781	−	0.798661i	$-0.705542\pi$
$277$	−5548.66			−1.20356			−0.601781	+	0.798661i	$0.705542\pi$
$278$	2491.90			0.537605
$279$	1342.45	−	2325.19i	0.288066	−	0.498944i
$280$	−725.866	−	1257.24i	−0.154924	−	0.268337i
$281$	22.8948	−	39.6549i	0.00486046	−	0.00841856i	−0.863585	−	0.504203i	$-0.831786\pi$
$281$	22.8948	−	39.6549i	0.00486046	−	0.00841856i	0.868445	+	0.495785i	$0.165120\pi$
$282$	331.099	+	573.480i	0.0699172	+	0.121100i
$283$	3060.37	+	5300.72i	0.642827	+	1.11341i	0.984799	+	0.173699i	$0.0555721\pi$
$283$	3060.37	+	5300.72i	0.642827	+	1.11341i	−0.341971	+	0.939710i	$0.611095\pi$
$284$	−1400.81			−0.292686
$285$	−2242.54	−	2027.27i	−0.466094	−	0.421351i
$286$	−8023.72			−1.65893
$287$	1051.55	+	1821.34i	0.216276	+	0.374601i
$288$	−382.293	−	662.150i	−0.0782181	−	0.135478i
$289$	1379.30	−	2389.02i	0.280746	−	0.486266i
$290$	1375.59	+	2382.58i	0.278542	+	0.482449i
$291$	−1054.71	+	1826.81i	−0.212468	+	0.368005i
$292$	−38.4224			−0.00770035
$293$	−7395.39			−1.47455			−0.737276	−	0.675592i	$-0.763888\pi$
$293$	−7395.39			−1.47455			−0.737276	+	0.675592i	$0.763888\pi$
$294$	−469.231	+	812.732i	−0.0930819	+	0.161223i
$295$	1925.83	−	3335.64i	0.380090	−	0.658334i
$296$	1512.14			0.296931
$297$	5577.61			1.08972
$298$	2272.01	−	3935.24i	0.441658	−	0.764975i
$299$	−1202.85	−	2083.39i	−0.232650	−	0.402962i
$300$	−1071.20	+	1855.38i	−0.206153	+	0.357067i
$301$	−737.258	−	1276.97i	−0.141179	−	0.244529i
$302$	3637.77	+	6300.80i	0.693146	+	1.20056i
$303$	1531.59			0.290388
$304$	−1261.06	+	406.978i	−0.237917	+	0.0767822i
$305$	−6391.76			−1.19997
$306$	1109.02	+	1920.88i	0.207184	+	0.358853i
$307$	287.534	+	498.024i	0.0534542	+	0.0925854i	0.891514	−	0.452992i	$-0.149644\pi$
$307$	287.534	+	498.024i	0.0534542	+	0.0925854i	−0.838060	+	0.545578i	$0.816310\pi$
$308$	1089.68	−	1887.38i	0.201592	−	0.349168i
$309$	1314.50	+	2276.79i	0.242005	+	0.419165i
$310$	−2327.10	+	4030.66i	−0.426357	+	0.738472i
$311$	−36.6434			−0.00668120			−0.00334060	−	0.999994i	$-0.501063\pi$
$311$	−36.6434			−0.00668120			−0.00334060	+	0.999994i	$0.501063\pi$
$312$	909.807			0.165089
$313$	2441.86	−	4229.43i	0.440966	−	0.763775i	−0.556795	−	0.830650i	$-0.687969\pi$
$313$	2441.86	−	4229.43i	0.440966	−	0.763775i	0.997761	+	0.0668742i	$0.0213026\pi$
$314$	−451.770	+	782.489i	−0.0811938	+	0.140632i
$315$	4335.83			0.775544
$316$	−4706.15			−0.837791
$317$	2933.65	−	5081.23i	0.519779	−	0.900284i	−0.479956	−	0.877292i	$-0.659348\pi$
$317$	2933.65	−	5081.23i	0.519779	−	0.900284i	0.999736	−	0.0229917i	$-0.00731913\pi$
$318$	−199.273	−	345.151i	−0.0351405	−	0.0608650i
$319$	−2065.05	+	3576.77i	−0.362447	+	0.627777i
$320$	662.695	+	1147.82i	0.115768	+	0.200516i
$321$	1419.04	+	2457.85i	0.246739	+	0.427364i
$322$	653.422			0.113086
$323$	3658.29	−	1180.63i	0.630195	−	0.203381i
$324$	1948.03			0.334025
$325$	9803.25	+	16979.7i	1.67319	+	2.89805i
$326$	215.631	+	373.484i	0.0366340	+	0.0634520i
$327$	44.9655	−	77.8825i	0.00760428	−	0.0131710i
$328$	−960.039	−	1662.84i	−0.161614	−	0.279923i
$329$	−823.018	+	1425.51i	−0.137916	+	0.238878i
$330$	−4539.22			−0.757200
$331$	−8866.06			−1.47227			−0.736137	−	0.676833i	$-0.763352\pi$
$331$	−8866.06			−1.47227			−0.736137	+	0.676833i	$0.763352\pi$
$332$	515.960	−	893.668i	0.0852921	−	0.147730i
$333$	−2258.13	+	3911.20i	−0.371606	+	0.643640i
$334$	6642.96			1.08828
$335$	−817.098			−0.133262
$336$	−123.559	+	214.010i	−0.0200615	+	0.0347476i
$337$	−1513.60	−	2621.63i	−0.244662	−	0.423767i	0.717375	−	0.696688i	$-0.245344\pi$
$337$	−1513.60	−	2621.63i	−0.244662	−	0.423767i	−0.962037	+	0.272921i	$0.912010\pi$
$338$	1966.11	−	3405.40i	0.316397	−	0.548016i
$339$	−1577.12	−	2731.64i	−0.252676	−	0.437648i
$340$	−1922.46	−	3329.79i	−0.306647	−	0.531128i
$341$	−6986.97			−1.10958
$342$	830.521	−	3869.52i	0.131314	−	0.611811i
$343$	−5338.32			−0.840356
$344$	673.096	+	1165.84i	0.105497	+	0.182726i
$345$	−680.481	−	1178.63i	−0.106191	−	0.183928i
$346$	1472.46	−	2550.37i	0.228785	−	0.396268i
$347$	4437.88	+	7686.63i	0.686564	+	1.18916i	0.972942	+	0.231048i	$0.0742153\pi$
$347$	4437.88	+	7686.63i	0.686564	+	1.18916i	−0.286378	+	0.958117i	$0.592451\pi$
$348$	234.155	−	405.569i	0.0360691	−	0.0624735i
$349$	2808.70			0.430791			0.215395	−	0.976527i	$-0.430896\pi$
$349$	2808.70			0.430791			0.215395	+	0.976527i	$0.430896\pi$
$350$	−5325.41			−0.813301
$351$	−2893.94	+	5012.46i	−0.440078	+	0.762237i
$352$	−994.849	+	1723.13i	−0.150641	+	0.260918i
$353$	11702.4			1.76446			0.882230	−	0.470819i	$-0.156041\pi$
$353$	11702.4			1.76446			0.882230	+	0.470819i	$0.156041\pi$
$354$	−655.640			−0.0984375
$355$	−3626.21	+	6280.78i	−0.542139	+	0.939012i
$356$	267.497	+	463.319i	0.0398239	+	0.0689771i
$357$	358.439	−	620.835i	0.0531390	−	0.0920394i
$358$	3573.98	+	6190.32i	0.527628	+	0.913879i
$359$	843.014	+	1460.14i	0.123935	+	0.214661i	0.921316	−	0.388815i	$-0.127115\pi$
$359$	843.014	+	1460.14i	0.123935	+	0.214661i	−0.797381	+	0.603476i	$0.793782\pi$
$360$	−3958.49			−0.579530
$361$	−6254.89	−	2814.66i	−0.911924	−	0.410359i
$362$	5887.46			0.854801
$363$	−2234.17	−	3869.70i	−0.323041	−	0.559523i
$364$	1130.76	+	1958.54i	0.162824	+	0.282020i
$365$	−99.4624	+	172.274i	−0.0142633	+	0.0247047i
$366$	544.011	+	942.254i	0.0776937	+	0.134569i
$367$	4218.01	−	7305.81i	0.599941	−	1.03913i	−0.392888	−	0.919586i	$-0.628524\pi$
$367$	4218.01	−	7305.81i	0.599941	−	1.03913i	0.992829	−	0.119542i	$-0.0381428\pi$
$368$	−596.556			−0.0845044
$369$	5734.62			0.809031
$370$	3914.42	−	6779.97i	0.550002	−	0.952632i
$371$	495.336	−	857.947i	0.0693169	−	0.120060i
$372$	792.250			0.110420
$373$	−1743.67			−0.242048			−0.121024	−	0.992650i	$-0.538618\pi$
$373$	−1743.67			−0.242048			−0.121024	+	0.992650i	$0.538618\pi$
$374$	2886.02	−	4998.74i	0.399018	−	0.691119i
$375$	3264.58	+	5654.42i	0.449553	+	0.778648i
$376$	751.393	−	1301.45i	0.103059	−	0.178503i
$377$	−2142.90	−	3711.62i	−0.292746	−	0.507050i
$378$	−786.038	−	1361.46i	−0.106956	−	0.185253i
$379$	−1591.45			−0.215693			−0.107846	−	0.994168i	$-0.534395\pi$
$379$	−1591.45			−0.215693			−0.107846	+	0.994168i	$0.534395\pi$
$380$	−1439.69	+	6707.72i	−0.194354	+	0.905523i
$381$	489.603			0.0658350
$382$	−700.359	−	1213.06i	−0.0938050	−	0.162475i
$383$	−4502.45	−	7798.48i	−0.600691	−	1.04043i	−0.992717	−	0.120473i	$-0.961559\pi$
$383$	−4502.45	−	7798.48i	−0.600691	−	1.04043i	0.392026	−	0.919954i	$-0.371774\pi$
$384$	112.806	−	195.385i	0.0149911	−	0.0259654i
$385$	−5641.61	−	9771.56i	−0.746814	−	1.29352i
$386$	−59.9015	+	103.753i	−0.00789873	+	0.0136810i
$387$	−4020.62			−0.528113
$388$	4787.10			0.626361
$389$	−2034.97	+	3524.66i	−0.265236	+	0.459402i	−0.967625	−	0.252391i	$-0.918783\pi$
$389$	−2034.97	+	3524.66i	−0.265236	+	0.459402i	0.702389	+	0.711793i	$0.252117\pi$
$390$	2355.18	−	4079.29i	0.305792	−	0.529648i
$391$	1730.59			0.223835
$392$	2129.74			0.274408
$393$	1606.32	−	2782.23i	0.206178	−	0.357111i
$394$	−374.382	−	648.448i	−0.0478707	−	0.0829145i
$395$	−12182.6	+	21100.9i	−1.55183	+	2.68785i
$396$	−2971.28	−	5146.40i	−0.377051	−	0.653072i
$397$	−164.785	−	285.416i	−0.0208321	−	0.0360822i	0.855421	−	0.517933i	$-0.173298\pi$
$397$	−164.785	−	285.416i	−0.0208321	−	0.0360822i	−0.876253	+	0.481850i	$0.839965\pi$
$398$	−9207.53			−1.15963
$399$	−1217.30	+	392.857i	−0.152735	+	0.0492918i
$400$	4861.96			0.607744
$401$	−4093.53	−	7090.20i	−0.509778	−	0.882962i	−0.999936	−	0.0113281i	$-0.996394\pi$
$401$	−4093.53	−	7090.20i	−0.509778	−	0.882962i	0.490158	−	0.871634i	$-0.336939\pi$
$402$	69.5442	+	120.454i	0.00862823	+	0.0149445i
$403$	3625.19	−	6279.02i	0.448098	−	0.776129i
$404$	−1737.89	−	3010.11i	−0.214017	−	0.370689i
$405$	5042.78	−	8734.35i	0.618710	−	1.07164i
$406$	1164.09			0.142297
$407$	11752.8			1.43136
$408$	−327.245	+	566.805i	−0.0397084	+	0.0687770i
$409$	−2499.25	+	4328.83i	−0.302152	+	0.523342i	−0.976623	−	0.214959i	$-0.931038\pi$
$409$	−2499.25	+	4328.83i	−0.302152	+	0.523342i	0.674472	+	0.738301i	$0.264372\pi$
$410$	−9940.83			−1.19742
$411$	1165.00			0.139819
$412$	2983.12	−	5166.92i	0.356718	−	0.617854i
$413$	−814.868	−	1411.39i	−0.0970873	−	0.168160i
$414$	890.855	−	1543.01i	0.105756	−	0.183175i
$415$	−2671.28	−	4626.80i	−0.315971	−	0.547278i
$416$	−1032.35	−	1788.09i	−0.121672	−	0.210741i
$417$	−2196.10			−0.257898
$418$	−9801.28	+	3163.14i	−1.14688	+	0.370130i
$419$	11941.1			1.39227			0.696134	−	0.717912i	$-0.254902\pi$
$419$	11941.1			1.39227			0.696134	+	0.717912i	$0.254902\pi$
$420$	639.701	+	1107.99i	0.0743195	+	0.128725i
$421$	5991.40	+	10377.4i	0.693594	+	1.20134i	0.970653	+	0.240486i	$0.0773069\pi$
$421$	5991.40	+	10377.4i	0.693594	+	1.20134i	−0.277059	+	0.960853i	$0.589360\pi$
$422$	−2956.72	+	5121.19i	−0.341069	+	0.590748i
$423$	2244.16	+	3886.99i	0.257954	+	0.446790i
$424$	−452.228	+	783.282i	−0.0517975	+	0.0897159i
$425$	−14104.4			−1.60979
$426$	1234.52			0.140406
$427$	−1352.26	+	2342.18i	−0.153256	+	0.265447i
$428$	3220.36	−	5577.83i	0.363696	−	0.629940i
$429$	7071.26			0.795812
$430$	6969.65			0.781643
$431$	−3541.49	+	6134.04i	−0.395795	+	0.685537i	−0.993202	−	0.116401i	$-0.962864\pi$
$431$	−3541.49	+	6134.04i	−0.395795	+	0.685537i	0.597407	+	0.801938i	$0.296198\pi$
$432$	717.631	+	1242.97i	0.0799237	+	0.138432i
$433$	3701.50	−	6411.19i	0.410815	−	0.711552i	−0.584164	−	0.811635i	$-0.698578\pi$
$433$	3701.50	−	6411.19i	0.410815	−	0.711552i	0.994979	+	0.100084i	$0.0319110\pi$
$434$	984.655	+	1705.47i	0.108905	+	0.188630i
$435$	−1212.29	−	2099.76i	−0.133621	−	0.231438i
$436$	−204.089			−0.0224176
$437$	−2290.64	−	2070.75i	−0.250747	−	0.226676i
$438$	33.8614			0.00369398
$439$	3837.72	+	6647.12i	0.417231	+	0.722665i	0.995660	−	0.0930680i	$-0.0296674\pi$
$439$	3837.72	+	6647.12i	0.417231	+	0.722665i	−0.578429	+	0.815733i	$0.696334\pi$
$440$	5150.64	+	8921.17i	0.558061	+	0.966591i
$441$	−3180.40	+	5508.62i	−0.343419	+	0.594819i
$442$	2994.83	+	5187.19i	0.322284	+	0.558211i
$443$	1341.94	−	2324.32i	0.143923	−	0.249281i	−0.785048	−	0.619435i	$-0.787362\pi$
$443$	1341.94	−	2324.32i	0.143923	−	0.249281i	0.928970	+	0.370154i	$0.120695\pi$
$444$	−1332.64			−0.142442
$445$	2769.83			0.295062
$446$	530.640	−	919.095i	0.0563375	−	0.0975794i
$447$	−2002.31	+	3468.10i	−0.211870	+	0.366970i
$448$	560.806			0.0591419
$449$	−14097.6			−1.48175			−0.740874	−	0.671644i	$-0.765589\pi$
$449$	−14097.6			−1.48175			−0.740874	+	0.671644i	$0.765589\pi$
$450$	−7260.51	+	12575.6i	−0.760586	+	1.31737i
$451$	−7461.67	−	12924.0i	−0.779060	−	1.34937i
$452$	−3579.09	+	6199.17i	−0.372448	+	0.645098i
$453$	−3205.94	−	5552.85i	−0.332513	−	0.575929i
$454$	−3479.72	−	6027.05i	−0.359717	−	0.623048i
$455$	11708.6			1.20639
$456$	1111.36	−	358.667i	0.114132	−	0.0368336i
$457$	7040.20			0.720627			0.360314	−	0.932831i	$-0.382670\pi$
$457$	7040.20			0.720627			0.360314	+	0.932831i	$0.382670\pi$
$458$	3566.48	+	6177.32i	0.363866	+	0.630234i
$459$	−2081.82	−	3605.82i	−0.211702	−	0.366678i
$460$	−1544.28	+	2674.77i	−0.156527	+	0.271112i
$461$	−3676.54	−	6367.96i	−0.371440	−	0.643352i	0.618348	−	0.785905i	$-0.287802\pi$
$461$	−3676.54	−	6367.96i	−0.371440	−	0.643352i	−0.989787	+	0.142552i	$0.954469\pi$
$462$	−960.329	+	1663.34i	−0.0967068	+	0.167501i
$463$	14054.7			1.41075			0.705377	−	0.708832i	$-0.250778\pi$
$463$	14054.7			1.41075			0.705377	+	0.708832i	$0.250778\pi$
$464$	−1062.78			−0.106333
$465$	2050.86	−	3552.20i	0.204530	−	0.354256i
$466$	−5991.20	+	10377.1i	−0.595573	+	1.03156i
$467$	5875.16			0.582163			0.291081	−	0.956698i	$-0.405985\pi$
$467$	5875.16			0.582163			0.291081	+	0.956698i	$0.405985\pi$
$468$	6166.59			0.609082
$469$	−172.867	+	299.415i	−0.0170198	+	0.0294791i
$470$	−3890.19	−	6738.01i	−0.381790	−	0.661279i
$471$	398.142	−	689.602i	0.0389499	−	0.0674633i
$472$	743.952	+	1288.56i	0.0725491	+	0.125659i
$473$	5231.48	+	9061.18i	0.508549	+	0.880832i
$474$	4147.50			0.401901
$475$	18668.8	+	16876.7i	1.80334	+	1.63022i
$476$	−1626.88			−0.156655
$477$	−1350.65	−	2339.40i	−0.129648	−	0.224557i
$478$	−606.478	−	1050.45i	−0.0580328	−	0.100516i
$479$	88.8904	−	153.963i	0.00847914	−	0.0146863i	−0.861755	−	0.507325i	$-0.830634\pi$
$479$	88.8904	−	153.963i	0.00847914	−	0.0146863i	0.870234	+	0.492639i	$0.163968\pi$
$480$	−584.029	−	1011.57i	−0.0555358	−	0.0961907i
$481$	−6097.92	+	10561.9i	−0.578049	+	1.00121i
$482$	6890.34			0.651133
$483$	−575.856			−0.0542492
$484$	−5070.22	+	8781.87i	−0.476166	+	0.824744i
$485$	12392.1	−	21463.8i	1.16020	−	2.00953i
$486$	−6560.80			−0.612353
$487$	12319.9			1.14634			0.573172	−	0.819435i	$-0.305713\pi$
$487$	12319.9			1.14634			0.573172	+	0.819435i	$0.305713\pi$
$488$	1234.57	−	2138.34i	0.114521	−	0.198357i
$489$	−190.034	−	329.149i	−0.0175739	−	0.0304389i
$490$	5513.15	−	9549.06i	0.508283	−	0.880372i
$491$	4220.92	+	7310.84i	0.387958	+	0.671963i	0.992175	−	0.124857i	$-0.0398473\pi$
$491$	4220.92	+	7310.84i	0.387958	+	0.671963i	−0.604217	+	0.796820i	$0.706514\pi$
$492$	846.076	+	1465.45i	0.0775285	+	0.134283i
$493$	3083.09			0.281654
$494$	2242.76	−	10449.4i	0.204265	−	0.951698i
$495$	−30766.4			−2.79363
$496$	−898.963	−	1557.05i	−0.0813803	−	0.140955i
$497$	1534.34	+	2657.55i	0.138480	+	0.239854i
$498$	−454.712	+	787.584i	−0.0409159	+	0.0708684i
$499$	3105.62	+	5379.09i	0.278610	+	0.482567i	0.971040	−	0.238918i	$-0.0767929\pi$
$499$	3105.62	+	5379.09i	0.278610	+	0.482567i	−0.692429	+	0.721486i	$0.743460\pi$
$500$	7408.61	−	12832.1i	0.662646	−	1.14774i
$501$	−5854.40			−0.522067
$502$	−3610.75			−0.321027
$503$	−7836.70	+	13573.6i	−0.694675	+	1.20321i	0.275616	+	0.961268i	$0.411118\pi$
$503$	−7836.70	+	13573.6i	−0.694675	+	1.20321i	−0.970290	+	0.241944i	$0.922215\pi$
$504$	−837.468	+	1450.54i	−0.0740155	+	0.128199i
$505$	−17995.1			−1.58569
$506$	−4636.59			−0.407354
$507$	−1732.72	+	3001.16i	−0.151781	+	0.262892i
$508$	−555.551	−	962.242i	−0.0485208	−	0.0840405i
$509$	9897.72	−	17143.3i	0.861903	−	1.49286i	−0.00818701	−	0.999966i	$-0.502606\pi$
$509$	9897.72	−	17143.3i	0.861903	−	1.49286i	0.870090	−	0.492893i	$-0.164061\pi$
$510$	1694.25	+	2934.52i	0.147103	+	0.254790i
$511$	42.0850	+	72.8933i	0.00364331	+	0.00631039i
$512$	−512.000			−0.0441942
$513$	−1559.03	+	7263.76i	−0.134177	+	0.625152i
$514$	−4473.93			−0.383923
$515$	−15444.5	−	26750.7i	−1.32149	−	2.28889i
$516$	−593.195	−	1027.44i	−0.0506085	−	0.0876564i
$517$	5840.02	−	10115.2i	0.496796	−	0.860476i
$518$	−1656.29	−	2868.77i	−0.140489	−	0.243333i
$519$	−1297.67	+	2247.62i	−0.109752	+	0.190096i
$520$	−10689.6			−0.901484
$521$	−21391.1			−1.79877			−0.899385	−	0.437157i	$-0.855986\pi$
$521$	−21391.1			−1.79877			−0.899385	+	0.437157i	$0.855986\pi$
$522$	1587.08	−	2748.91i	0.133074	−	0.230491i
$523$	−1601.07	+	2773.13i	−0.133862	+	0.231855i	−0.925162	−	0.379572i	$-0.876071\pi$
$523$	−1601.07	+	2773.13i	−0.133862	+	0.231855i	0.791300	+	0.611428i	$0.209404\pi$
$524$	−7290.73			−0.607819
$525$	4693.25			0.390153
$526$	832.258	−	1441.51i	0.0689890	−	0.119492i
$527$	2607.86	+	4516.95i	0.215560	+	0.373361i
$528$	876.754	−	1518.58i	0.0722648	−	0.125166i
$529$	5388.42	+	9333.02i	0.442872	+	0.767077i
$530$	2341.32	+	4055.29i	0.191888	+	0.332360i
$531$	−4443.87			−0.363178
$532$	2153.37	+	1946.65i	0.175490	+	0.158643i
$533$	15485.9			1.25848
$534$	−235.743	−	408.320i	−0.0191042	−	0.0330894i
$535$	−16672.8	−	28878.1i	−1.34734	−	2.33366i
$536$	157.823	−	273.357i	0.0127181	−	0.0220284i
$537$	−3149.73	−	5455.49i	−0.253111	−	0.438402i
$538$	−3483.89	+	6034.27i	−0.279184	+	0.483561i
$539$	16552.9			1.32279
$540$	7430.79			0.592167
$541$	3681.50	−	6376.55i	0.292569	−	0.506745i	−0.681847	−	0.731495i	$-0.738823\pi$
$541$	3681.50	−	6376.55i	0.292569	−	0.506745i	0.974417	+	0.224750i	$0.0721564\pi$
$542$	1789.11	−	3098.82i	0.141787	−	0.245583i
$543$	−5188.58			−0.410061
$544$	1485.29			0.117062
$545$	−528.315	+	915.068i	−0.0415239	+	0.0719215i
$546$	−996.533	−	1726.05i	−0.0781093	−	0.135289i
$547$	6484.65	−	11231.7i	0.506880	−	0.877942i	−0.493088	−	0.869979i	$-0.664132\pi$
$547$	6484.65	−	11231.7i	0.506880	−	0.877942i	0.999968	−	0.00796294i	$-0.00253471\pi$
$548$	−1321.93	−	2289.64i	−0.103047	−	0.178483i
$549$	3687.25	+	6386.50i	0.286645	+	0.496483i
$550$	37788.4			2.92964
$551$	−4080.84	−	3689.10i	−0.315517	−	0.285228i
$552$	525.741			0.0405381
$553$	5154.76	+	8928.31i	0.396388	+	0.686565i
$554$	−5548.66	−	9610.56i	−0.425523	−	0.737028i
$555$	−3449.75	+	5975.14i	−0.263845	+	0.456992i
$556$	2491.90	+	4316.10i	0.190072	+	0.329215i
$557$	−9997.27	+	17315.8i	−0.760499	+	1.31722i	0.182095	+	0.983281i	$0.441712\pi$
$557$	−9997.27	+	17315.8i	−0.760499	+	1.31722i	−0.942594	+	0.333942i	$0.891621\pi$
$558$	5369.80			0.407386
$559$	−10857.4			−0.821502
$560$	1451.73	−	2514.47i	0.109548	−	0.189743i
$561$	−2543.43	+	4405.35i	−0.191415	+	0.331540i
$562$	91.5792			0.00687372
$563$	−15654.6			−1.17187			−0.585936	−	0.810358i	$-0.699273\pi$
$563$	−15654.6			−1.17187			−0.585936	+	0.810358i	$0.699273\pi$
$564$	−662.198	+	1146.96i	−0.0494389	+	0.0856307i
$565$	18530.1	+	32095.0i	1.37976	+	2.38982i
$566$	−6120.74	+	10601.4i	−0.454548	+	0.787300i
$567$	−2133.72	−	3695.72i	−0.158039	−	0.273731i
$568$	−1400.81	−	2426.27i	−0.103480	−	0.179233i
$569$	−6450.45			−0.475249			−0.237625	−	0.971357i	$-0.576369\pi$
$569$	−6450.45			−0.475249			−0.237625	+	0.971357i	$0.576369\pi$
$570$	1268.79	−	5911.47i	0.0932345	−	0.434393i
$571$	18704.6			1.37086			0.685431	−	0.728138i	$-0.259614\pi$
$571$	18704.6			1.37086			0.685431	+	0.728138i	$0.259614\pi$
$572$	−8023.72	−	13897.5i	−0.586519	−	1.01588i
$573$	617.222	+	1069.06i	0.0449997	+	0.0779418i
$574$	−2103.11	+	3642.69i	−0.152930	+	0.264883i
$575$	5664.90	+	9811.90i	0.410857	+	0.711625i
$576$	764.585	−	1324.30i	0.0553085	−	0.0957972i
$577$	−12394.4			−0.894257			−0.447128	−	0.894470i	$-0.647553\pi$
$577$	−12394.4			−0.894257			−0.447128	+	0.894470i	$0.647553\pi$
$578$	5517.21			0.397034
$579$	52.7908	−	91.4364i	0.00378914	−	0.00656298i
$580$	−2751.17	+	4765.17i	−0.196959	+	0.341143i
$581$	−2260.57			−0.161419
$582$	−4218.84			−0.300475
$583$	−3514.83	+	6087.87i	−0.249690	+	0.432476i
$584$	−38.4224	−	66.5496i	−0.00272248	−	0.00471548i
$585$	15963.2	−	27649.0i	1.12820	−	1.95409i
$586$	−7395.39	−	12809.2i	−0.521333	−	0.902974i
$587$	3212.31	+	5563.88i	0.225871	+	0.391220i	0.956580	−	0.291469i	$-0.0941440\pi$
$587$	3212.31	+	5563.88i	0.225871	+	0.391220i	−0.730710	+	0.682688i	$0.760811\pi$
$588$	−1876.92			−0.131638
$589$	1952.97	−	9099.19i	0.136623	−	0.636546i
$590$	7703.34			0.537528
$591$	329.940	+	571.473i	0.0229643	+	0.0397754i
$592$	1512.14	+	2619.11i	0.104981	+	0.181832i
$593$	−9050.05	+	15675.2i	−0.626714	+	1.08550i	0.361493	+	0.932375i	$0.382267\pi$
$593$	−9050.05	+	15675.2i	−0.626714	+	1.08550i	−0.988207	+	0.153125i	$0.951066\pi$
$594$	5577.61	+	9660.70i	0.385273	+	0.667312i
$595$	−4211.42	+	7294.40i	−0.290171	+	0.502590i
$596$	9088.05			0.624599
$597$	8114.54			0.556291
$598$	2405.69	−	4166.78i	0.164509	−	0.284937i
$599$	1423.60	−	2465.74i	0.0971061	−	0.168193i	−0.813380	−	0.581733i	$-0.802375\pi$
$599$	1423.60	−	2465.74i	0.0971061	−	0.168193i	0.910486	+	0.413541i	$0.135708\pi$
$600$	−4284.81			−0.291544
$601$	6934.19			0.470635			0.235317	−	0.971919i	$-0.424387\pi$
$601$	6934.19			0.470635			0.235317	+	0.971919i	$0.424387\pi$
$602$	1474.52	−	2553.94i	0.0998286	−	0.172908i
$603$	471.364	+	816.426i	0.0318332	+	0.0551367i
$604$	−7275.53	+	12601.6i	−0.490128	+	0.848926i
$605$	26250.1	+	45466.5i	1.76400	+	3.05533i
$606$	1531.59	+	2652.79i	0.102667	+	0.177825i
$607$	9089.78			0.607813			0.303907	−	0.952702i	$-0.401709\pi$
$607$	9089.78			0.607813			0.303907	+	0.952702i	$0.401709\pi$
$608$	−1965.97	−	1777.24i	−0.131136	−	0.118547i
$609$	−1025.90			−0.0682622
$610$	−6391.76	−	11070.9i	−0.424254	−	0.734829i
$611$	6060.19	+	10496.6i	0.401259	+	0.695000i
$612$	−2218.04	+	3841.75i	−0.146501	+	0.253748i
$613$	−12818.6	−	22202.5i	−0.844598	−	1.46289i	−0.885970	−	0.463743i	$-0.846506\pi$
$613$	−12818.6	−	22202.5i	−0.844598	−	1.46289i	0.0413712	−	0.999144i	$-0.486827\pi$
$614$	−575.069	+	996.048i	−0.0377979	+	0.0654678i
$615$	8760.79			0.574421
$616$	4358.72			0.285094
$617$	−10891.1	+	18863.9i	−0.710630	+	1.23085i	0.253991	+	0.967207i	$0.418257\pi$
$617$	−10891.1	+	18863.9i	−0.710630	+	1.23085i	−0.964621	+	0.263641i	$0.915077\pi$
$618$	−2629.01	+	4553.57i	−0.171123	+	0.296394i
$619$	−23717.7			−1.54006			−0.770029	−	0.638008i	$-0.779758\pi$
$619$	−23717.7			−1.54006			−0.770029	+	0.638008i	$0.779758\pi$
$620$	−9308.42			−0.602960
$621$	−1672.29	+	2896.50i	−0.108062	+	0.187170i
$622$	−36.6434	−	63.4682i	−0.00236216	−	0.00409138i
$623$	585.992	−	1014.97i	0.0376842	−	0.0652710i
$624$	909.807	+	1575.83i	0.0583677	+	0.101096i
$625$	−19364.7	−	33540.6i	−1.23934	−	2.14660i
$626$	9767.46			0.623620
$627$	8637.81	−	2787.65i	0.550177	−	0.177557i
$628$	−1807.08			−0.114825
$629$	−4386.68	−	7597.95i	−0.278074	−	0.481638i
$630$	4335.83	+	7509.88i	0.274196	+	0.474922i
$631$	13101.6	−	22692.6i	0.826571	−	1.43166i	−0.0741409	−	0.997248i	$-0.523621\pi$
$631$	13101.6	−	22692.6i	0.826571	−	1.43166i	0.900712	−	0.434416i	$-0.143045\pi$
$632$	−4706.15	−	8151.30i	−0.296204	−	0.513040i
$633$	2605.74	−	4513.28i	0.163616	−	0.283391i
$634$	11734.6			0.735079
$635$	−5752.51			−0.359498
$636$	398.546	−	690.301i	0.0248481	−	0.0430381i
$637$	−8588.45	+	14875.6i	−0.534202	+	0.925265i
$638$	−8260.20			−0.512577
$639$	8367.48			0.518016
$640$	−1325.39	+	2295.64i	−0.0818604	+	0.141786i
$641$	−2092.66	−	3624.59i	−0.128947	−	0.223343i	0.794322	−	0.607497i	$-0.207826\pi$
$641$	−2092.66	−	3624.59i	−0.128947	−	0.223343i	−0.923269	+	0.384154i	$0.874493\pi$
$642$	−2838.08	+	4915.70i	−0.174471	+	0.302192i
$643$	−16099.1	−	27884.5i	−0.987383	−	1.71020i	−0.630827	−	0.775924i	$-0.717284\pi$
$643$	−16099.1	−	27884.5i	−0.987383	−	1.71020i	−0.356556	−	0.934274i	$-0.616049\pi$
$644$	653.422	+	1131.76i	0.0399820	+	0.0692509i
$645$	−6142.31			−0.374966
$646$	5703.20	+	5155.72i	0.347352	+	0.314008i
$647$	371.159			0.0225530			0.0112765	−	0.999936i	$-0.496411\pi$
$647$	371.159			0.0225530			0.0112765	+	0.999936i	$0.496411\pi$
$648$	1948.03	+	3374.09i	0.118096	+	0.204547i
$649$	5782.19	+	10015.0i	0.349724	+	0.605739i
$650$	−19606.5	+	33959.4i	−1.18312	+	2.04923i
$651$	−867.770	−	1503.02i	−0.0522436	−	0.0904886i
$652$	−431.262	+	746.968i	−0.0259042	+	0.0448674i
$653$	1659.89			0.0994741			0.0497370	−	0.998762i	$-0.484162\pi$
$653$	1659.89			0.0994741			0.0497370	+	0.998762i	$0.484162\pi$
$654$	179.862			0.0107541
$655$	−18873.2	+	32689.3i	−1.12586	+	1.95004i
$656$	1920.08	−	3325.67i	0.114278	−	0.197935i
$657$	229.510			0.0136286
$658$	−3292.07			−0.195043
$659$	12365.0	−	21416.8i	0.730914	−	1.26598i	−0.225578	−	0.974225i	$-0.572427\pi$
$659$	12365.0	−	21416.8i	0.730914	−	1.26598i	0.956493	−	0.291756i	$-0.0942395\pi$
$660$	−4539.22	−	7862.17i	−0.267711	−	0.463688i
$661$	4199.93	−	7274.48i	0.247138	−	0.428055i	−0.715593	−	0.698518i	$-0.753843\pi$
$661$	4199.93	−	7274.48i	0.247138	−	0.428055i	0.962731	+	0.270462i	$0.0871766\pi$
$662$	−8866.06	−	15356.5i	−0.520527	−	0.901580i
$663$	−2639.32	−	4571.44i	−0.154604	−	0.267783i
$664$	2063.84			0.120621
$665$	14302.5	−	4615.81i	0.834026	−	0.269163i
$666$	−9032.52			−0.525530
$667$	−1238.30	−	2144.79i	−0.0718846	−	0.124508i
$668$	6642.96	+	11506.0i	0.384766	+	0.666435i
$669$	−467.649	+	809.993i	−0.0270260	+	0.0468104i
$670$	−817.098	−	1415.26i	−0.0471153	−	0.0816061i
$671$	9595.41	−	16619.7i	0.552052	−	0.956182i
$672$	−494.234			−0.0283713
$673$	27850.0			1.59516			0.797578	−	0.603216i	$-0.206114\pi$
$673$	27850.0			1.59516			0.797578	+	0.603216i	$0.206114\pi$
$674$	3027.20	−	5243.27i	0.173002	−	0.299649i
$675$	13629.3	−	23606.6i	0.777171	−	1.34610i
$676$	7864.44			0.447453
$677$	20343.1			1.15487			0.577437	−	0.816435i	$-0.304053\pi$
$677$	20343.1			1.15487			0.577437	+	0.816435i	$0.304053\pi$
$678$	3154.23	−	5463.29i	0.178669	−	0.309464i
$679$	−5243.42	−	9081.86i	−0.296353	−	0.513299i
$680$	3844.91	−	6659.59i	0.216832	−	0.375564i
$681$	3066.66	+	5311.60i	0.172562	+	0.298886i
$682$	−6986.97	−	12101.8i	−0.392295	−	0.679474i
$683$	−26794.4			−1.50111			−0.750556	−	0.660807i	$-0.770214\pi$
$683$	−26794.4			−1.50111			−0.750556	+	0.660807i	$0.770214\pi$
$684$	7532.72	−	2431.01i	0.421083	−	0.135895i
$685$	−13688.0			−0.763493
$686$	−5338.32	−	9246.24i	−0.297111	−	0.514611i
$687$	−3143.11	−	5444.03i	−0.174552	−	0.302333i
$688$	−1346.19	+	2331.67i	−0.0745975	+	0.129207i
$689$	−3647.34	−	6317.38i	−0.201673	−	0.349308i
$690$	1360.96	−	2357.25i	0.0750883	−	0.130057i
$691$	29092.3			1.60162			0.800812	−	0.598916i	$-0.204402\pi$
$691$	29092.3			1.60162			0.800812	+	0.598916i	$0.204402\pi$
$692$	5889.83			0.323552
$693$	−6509.02	+	11273.9i	−0.356792	+	0.617982i
$694$	−8875.76	+	15373.3i	−0.485474	+	0.840866i
$695$	25802.7			1.40827
$696$	936.621			0.0510094
$697$	−5570.08	+	9647.66i	−0.302700	+	0.524291i
$698$	2808.70	+	4864.80i	0.152308	+	0.263804i
$699$	5280.00	−	9145.23i	0.285705	−	0.494856i
$700$	−5325.41	−	9223.89i	−0.287545	−	0.498043i
$701$	−10761.5	−	18639.5i	−0.579824	−	1.00428i	−0.995499	−	0.0947713i	$-0.969788\pi$
$701$	−10761.5	−	18639.5i	−0.579824	−	1.00428i	0.415675	−	0.909513i	$-0.363545\pi$
$702$	−11575.8			−0.622364
$703$	−3285.09	+	15305.7i	−0.176244	+	0.821147i
$704$	−3979.39			−0.213038
$705$	3428.40	+	5938.17i	0.183150	+	0.317226i
$706$	11702.4	+	20269.1i	0.623831	+	1.08051i
$707$	−3807.09	+	6594.08i	−0.202518	+	0.350772i
$708$	−655.640	−	1135.60i	−0.0348029	−	0.0602804i
$709$	−7482.91	+	12960.8i	−0.396370	+	0.686533i	−0.993275	−	0.115779i	$-0.963064\pi$
$709$	−7482.91	+	12960.8i	−0.396370	+	0.686533i	0.596905	+	0.802312i	$0.296397\pi$
$710$	−14504.8			−0.766700
$711$	28111.4			1.48278
$712$	−534.994	+	926.637i	−0.0281598	+	0.0487742i
$713$	2094.85	−	3628.39i	0.110032	−	0.190581i
$714$	1433.76			0.0751499
$715$	−83082.6			−4.34561
$716$	−7147.97	+	12380.6i	−0.373090	+	0.646210i
$717$	534.485	+	925.756i	0.0278392	+	0.0482189i
$718$	−1686.03	+	2920.29i	−0.0876351	+	0.151788i
$719$	−3678.90	−	6372.03i	−0.190820	−	0.330510i	0.754702	−	0.656068i	$-0.227781\pi$
$719$	−3678.90	−	6372.03i	−0.190820	−	0.330510i	−0.945522	+	0.325557i	$0.894448\pi$
$720$	−3958.49	−	6856.31i	−0.204895	−	0.354888i
$721$	−13069.9			−0.675104
$722$	−1379.76	−	13648.4i	−0.0711210	−	0.703521i
$723$	−6072.41			−0.312359
$724$	5887.46	+	10197.4i	0.302218	+	0.523457i
$725$	10092.2	+	17480.1i	0.516984	+	0.895443i
$726$	4468.35	−	7739.41i	0.228424	−	0.395642i
$727$	−14574.2	−	25243.2i	−0.743503	−	1.28779i	−0.950891	−	0.309527i	$-0.899829\pi$
$727$	−14574.2	−	25243.2i	−0.743503	−	1.28779i	0.207387	−	0.978259i	$-0.433504\pi$
$728$	−2261.52	+	3917.08i	−0.115134	+	0.199418i
$729$	−7367.23			−0.374294
$730$	−397.849			−0.0201713
$731$	3905.26	−	6764.11i	0.197594	−	0.342243i
$732$	−1088.02	+	1884.51i	−0.0549377	+	0.0951549i
$733$	21514.5			1.08412			0.542059	−	0.840341i	$-0.317645\pi$
$733$	21514.5			1.08412			0.542059	+	0.840341i	$0.317645\pi$
$734$	16872.1			0.848445
$735$	−4858.70	+	8415.52i	−0.243831	+	0.422328i
$736$	−596.556	−	1033.27i	−0.0298768	−	0.0517482i
$737$	1226.64	−	2124.60i	0.0613079	−	0.106188i
$738$	5734.62	+	9932.65i	0.286036	+	0.495428i
$739$	11558.0	+	20019.0i	0.575326	+	0.996495i	0.996006	+	0.0892854i	$0.0284583\pi$
$739$	11558.0	+	20019.0i	0.575326	+	0.996495i	−0.420680	+	0.907209i	$0.638208\pi$
$740$	15657.7			0.777821
$741$	−1976.53	+	9208.95i	−0.0979889	+	0.456544i
$742$	1981.34			0.0980289
$743$	−7551.47	−	13079.5i	−0.372862	−	0.645816i	0.617142	−	0.786852i	$-0.288290\pi$
$743$	−7551.47	−	13079.5i	−0.372862	−	0.645816i	−0.990005	+	0.141035i	$0.954957\pi$
$744$	792.250	+	1372.22i	0.0390394	+	0.0676182i
$745$	23525.8	−	40747.9i	1.15694	−	2.00388i
$746$	−1743.67	−	3020.13i	−0.0855770	−	0.148224i
$747$	−3081.99	+	5338.17i	−0.150956	+	0.261464i
$748$	11544.1			0.564296
$749$	−14109.3			−0.688310
$750$	−6529.16	+	11308.8i	−0.317882	+	0.550587i
$751$	−14297.9	+	24764.7i	−0.694726	+	1.20330i	0.275547	+	0.961288i	$0.411141\pi$
$751$	−14297.9	+	24764.7i	−0.694726	+	1.20330i	−0.970273	+	0.242013i	$0.922192\pi$
$752$	3005.57			0.145747
$753$	3182.13			0.154002
$754$	4285.81	−	7423.23i	0.207002	−	0.358539i
$755$	37667.7	+	65242.3i	1.81572	+	3.14492i
$756$	1572.08	−	2722.91i	0.0756294	−	0.130994i
$757$	3822.82	+	6621.32i	0.183544	+	0.317908i	0.943085	−	0.332552i	$-0.107910\pi$
$757$	3822.82	+	6621.32i	0.183544	+	0.317908i	−0.759541	+	0.650460i	$0.774576\pi$
$758$	−1591.45	−	2756.48i	−0.0762589	−	0.132084i
$759$	4086.19			0.195414
$760$	−13057.8	+	4214.10i	−0.623231	+	0.201134i
$761$	10724.9			0.510876			0.255438	−	0.966825i	$-0.417780\pi$
$761$	10724.9			0.510876			0.255438	+	0.966825i	$0.417780\pi$
$762$	489.603	+	848.018i	0.0232762	+	0.0403155i
$763$	223.543	+	387.188i	0.0106066	+	0.0183711i
$764$	1400.72	−	2426.12i	0.0663301	−	0.114887i
$765$	11483.5	+	19889.9i	0.542726	+	0.940028i
$766$	9004.90	−	15597.0i	0.424752	−	0.735693i
$767$	−12000.4			−0.564938
$768$	451.222			0.0212006
$769$	1981.77	−	3432.52i	0.0929315	−	0.160962i	−0.815812	−	0.578317i	$-0.803710\pi$
$769$	1981.77	−	3432.52i	0.0929315	−	0.160962i	0.908743	+	0.417355i	$0.137043\pi$
$770$	11283.2	−	19543.1i	0.528077	−	0.914656i
$771$	3942.85			0.184174
$772$	−239.606			−0.0111705
$773$	2222.65	−	3849.74i	0.103419	−	0.179128i	−0.809672	−	0.586883i	$-0.800355\pi$
$773$	2222.65	−	3849.74i	0.103419	−	0.179128i	0.913091	+	0.407755i	$0.133688\pi$
$774$	−4020.62	−	6963.92i	−0.186716	−	0.323402i
$775$	−17073.1	+	29571.5i	−0.791335	+	1.37063i
$776$	4787.10	+	8291.49i	0.221452	+	0.383566i
$777$	1459.67	+	2528.23i	0.0673945	+	0.116731i
$778$	−8139.86			−0.375100
$779$	18916.7	−	6104.92i	0.870038	−	0.280785i
$780$	9420.71			0.432456
$781$	−10887.4	−	18857.6i	−0.498826	−	0.863992i
$782$	1730.59	+	2997.47i	0.0791378	+	0.137071i
$783$	−2979.23	+	5160.18i	−0.135976	+	0.235517i
$784$	2129.74	+	3688.81i	0.0970179	+	0.168040i
$785$	−4677.91	+	8102.37i	−0.212690	+	0.368390i
$786$	6425.28			0.291580
$787$	3452.08			0.156357			0.0781787	−	0.996939i	$-0.475090\pi$
$787$	3452.08			0.156357			0.0781787	+	0.996939i	$0.475090\pi$
$788$	748.763	−	1296.90i	0.0338497	−	0.0586294i
$789$	−733.464	+	1270.40i	−0.0330951	+	0.0573223i
$790$	−48730.4			−2.19462
$791$	15681.1			0.704872
$792$	5942.55	−	10292.8i	0.266615	−	0.461791i
$793$	9957.16	+	17246.3i	0.445888	+	0.772301i
$794$	329.570	−	570.832i	0.0147305	−	0.0255140i
$795$	−2063.39	−	3573.90i	−0.0920516	−	0.159438i
$796$	−9207.53	−	15947.9i	−0.409990	−	0.710124i
$797$	−25298.0			−1.12434			−0.562171	−	0.827021i	$-0.690034\pi$
$797$	−25298.0			−1.12434			−0.562171	+	0.827021i	$0.690034\pi$
$798$	−1897.75	−	1715.57i	−0.0841850	−	0.0761036i
$799$	−8719.06			−0.386055
$800$	4861.96	+	8421.15i	0.214870	+	0.372166i
$801$	−1597.85	−	2767.55i	−0.0704833	−	0.122081i
$802$	8187.06	−	14180.4i	0.360468	−	0.624348i
$803$	−298.629	−	517.240i	−0.0131238	−	0.0227310i
$804$	−139.088	+	240.908i	−0.00610108	+	0.0105674i
$805$	6765.93			0.296233
$806$	14500.8			0.633707
$807$	3070.33	−	5317.96i	0.133929	−	0.231972i
$808$	3475.77	−	6020.21i	0.151333	−	0.262117i
$809$	−23140.8			−1.00567			−0.502834	−	0.864383i	$-0.667709\pi$
$809$	−23140.8			−1.00567			−0.502834	+	0.864383i	$0.667709\pi$
$810$	20171.1			0.874989
$811$	5554.38	−	9620.46i	0.240494	−	0.416548i	−0.720361	−	0.693599i	$-0.756024\pi$
$811$	5554.38	−	9620.46i	0.240494	−	0.416548i	0.960855	+	0.277051i	$0.0893572\pi$
$812$	1164.09	+	2016.26i	0.0503097	+	0.0871390i
$813$	−1576.73	+	2730.97i	−0.0680176	+	0.117810i
$814$	11752.8	+	20356.4i	0.506062	+	0.876525i
$815$	2232.78	+	3867.28i	0.0959641	+	0.166215i
$816$	−1308.98			−0.0561562
$817$	−13262.7	+	4280.24i	−0.567937	+	0.183289i
$818$	−9997.00			−0.427307
$819$	−6754.41	−	11699.0i	−0.288178	−	0.499140i
$820$	−9940.83	−	17218.0i	−0.423352	−	0.733268i
$821$	−6204.51	+	10746.5i	−0.263750	+	0.456829i	−0.967235	−	0.253881i	$-0.918293\pi$
$821$	−6204.51	+	10746.5i	−0.263750	+	0.456829i	0.703485	+	0.710710i	$0.251626\pi$
$822$	1165.00	+	2017.85i	0.0494333	+	0.0856211i
$823$	9536.05	−	16516.9i	0.403895	−	0.699567i	−0.590297	−	0.807186i	$-0.700989\pi$
$823$	9536.05	−	16516.9i	0.403895	−	0.699567i	0.994192	+	0.107619i	$0.0343226\pi$
$824$	11932.5			0.504476
$825$	−33302.6			−1.40539
$826$	1629.74	−	2822.79i	0.0686511	−	0.118907i
$827$	−2143.56	+	3712.76i	−0.0901317	+	0.156113i	−0.907566	−	0.419909i	$-0.862062\pi$
$827$	−2143.56	+	3712.76i	−0.0901317	+	0.156113i	0.817435	+	0.576021i	$0.195395\pi$
$828$	3563.42			0.149562
$829$	−22544.9			−0.944533			−0.472266	−	0.881456i	$-0.656564\pi$
$829$	−22544.9			−0.944533			−0.472266	+	0.881456i	$0.656564\pi$
$830$	5342.56	−	9253.59i	0.223425	−	0.386984i
$831$	4890.00	+	8469.72i	0.204130	+	0.353564i
$832$	2064.71	−	3576.18i	0.0860348	−	0.149017i
$833$	−6178.29	−	10701.1i	−0.256981	−	0.445104i
$834$	−2196.10	−	3803.75i	−0.0911805	−	0.157929i
$835$	68785.3			2.85080
$836$	−15280.0	−	13813.2i	−0.632141	−	0.571458i
$837$	−10080.1			−0.416270
$838$	11941.1	+	20682.6i	0.492241	+	0.852587i
$839$	−19298.9	−	33426.7i	−0.794127	−	1.37547i	−0.923392	−	0.383858i	$-0.874595\pi$
$839$	−19298.9	−	33426.7i	−0.794127	−	1.37547i	0.129266	−	0.991610i	$-0.458738\pi$
$840$	−1279.40	+	2215.99i	−0.0525518	+	0.0910225i
$841$	9988.44	+	17300.5i	0.409547	+	0.709356i
$842$	−11982.8	+	20754.8i	−0.490445	+	0.849475i
$843$	−80.7081			−0.00329743
$844$	−11826.9			−0.482344
$845$	20358.3	−	35261.6i	0.828813	−	1.43555i
$846$	−4488.31	+	7773.98i	−0.182401	+	0.315928i
$847$	22214.1			0.901164
$848$	−1808.91			−0.0732527
$849$	5394.17	−	9342.98i	0.218054	−	0.377680i
$850$	−14104.4	−	24429.5i	−0.569148	−	0.985793i
$851$	−3523.74	+	6103.30i	−0.141942	+	0.245850i
$852$	1234.52	+	2138.26i	0.0496409	+	0.0859806i
$853$	−1804.94	−	3126.25i	−0.0724502	−	0.125488i	0.827524	−	0.561430i	$-0.189749\pi$
$853$	−1804.94	−	3126.25i	−0.0724502	−	0.125488i	−0.899975	+	0.435942i	$0.856415\pi$
$854$	−5409.03			−0.216737
$855$	8599.72	−	40067.3i	0.343982	−	1.60266i
$856$	12881.4			0.514344
$857$	1209.06	+	2094.15i	0.0481921	+	0.0834711i	0.889115	−	0.457683i	$-0.151321\pi$
$857$	1209.06	+	2094.15i	0.0481921	+	0.0834711i	−0.840923	+	0.541155i	$0.817987\pi$
$858$	7071.26	+	12247.8i	0.281362	+	0.487333i
$859$	−17426.1	+	30183.0i	−0.692168	+	1.19887i	0.278958	+	0.960303i	$0.410011\pi$
$859$	−17426.1	+	30183.0i	−0.692168	+	1.19887i	−0.971126	+	0.238567i	$0.923322\pi$
$860$	6969.65	+	12071.8i	0.276353	+	0.478657i
$861$	1853.45	−	3210.28i	0.0733630	−	0.127068i
$862$	−14166.0			−0.559739
$863$	−32080.0			−1.26537			−0.632685	−	0.774409i	$-0.718047\pi$
$863$	−32080.0			−1.26537			−0.632685	+	0.774409i	$0.718047\pi$
$864$	−1435.26	+	2485.95i	−0.0565146	+	0.0978861i
$865$	15246.7	−	26408.1i	0.599311	−	1.03804i
$866$	14806.0			0.580980
$867$	−4862.28			−0.190463
$868$	−1969.31	+	3410.95i	−0.0770078	+	0.133381i
$869$	−36577.4	−	63354.0i	−1.42785	−	2.47311i
$870$	2424.59	−	4199.51i	0.0944842	−	0.163651i
$871$	1272.89	+	2204.70i	0.0495179	+	0.0857675i
$872$	−204.089	−	353.492i	−0.00792582	−	0.0137279i
$873$	−28594.9			−1.10858
$874$	1296.00	−	6038.26i	0.0501578	−	0.233693i
$875$	−32459.3			−1.25409
$876$	33.8614	+	58.6497i	0.00130602	+	0.00226209i
$877$	−21507.3	−	37251.7i	−0.828107	−	1.43432i	−0.899521	−	0.436877i	$-0.856084\pi$
$877$	−21507.3	−	37251.7i	−0.828107	−	1.43432i	0.0714140	−	0.997447i	$-0.477249\pi$
$878$	−7675.43	+	13294.2i	−0.295027	+	0.511001i
$879$	6517.51	+	11288.7i	0.250091	+	0.433171i
$880$	−10301.3	+	17842.3i	−0.394609	+	0.683483i
$881$	20270.3			0.775170			0.387585	−	0.921834i	$-0.373309\pi$
$881$	20270.3			0.775170			0.387585	+	0.921834i	$0.373309\pi$
$882$	−12721.6			−0.485667
$883$	9829.17	−	17024.6i	0.374607	−	0.648838i	−0.615661	−	0.788011i	$-0.711111\pi$
$883$	9829.17	−	17024.6i	0.374607	−	0.648838i	0.990268	+	0.139173i	$0.0444443\pi$
$884$	−5989.65	+	10374.4i	−0.227889	+	0.394715i
$885$	−6788.90			−0.257860
$886$	5367.78			0.203537
$887$	−22422.7	+	38837.3i	−0.848795	+	1.47016i	0.0334891	+	0.999439i	$0.489338\pi$
$887$	−22422.7	+	38837.3i	−0.848795	+	1.47016i	−0.882284	+	0.470717i	$0.843995\pi$
$888$	−1332.64	−	2308.20i	−0.0503610	−	0.0872278i
$889$	−1217.02	+	2107.93i	−0.0459138	+	0.0795251i
$890$	2769.83	+	4797.49i	0.104320	+	0.180688i
$891$	15140.6	+	26224.3i	0.569281	+	0.986023i
$892$	2122.56			0.0796733
$893$	11540.7	+	10432.9i	0.432470	+	0.390955i
$894$	−8009.24			−0.299630
$895$	37007.2	+	64098.4i	1.38214	+	2.39394i
$896$	560.806	+	971.344i	0.0209098	+	0.0362169i
$897$	−2120.12	+	3672.16i	−0.0789173	+	0.136689i
$898$	−14097.6	−	24417.7i	−0.523877	−	0.907382i
$899$	3732.03	−	6464.07i	0.138454	−	0.239810i
$900$	−29042.0			−1.07563
$901$	5247.59			0.194032
$902$	14923.3	−	25848.0i	0.550879	−	0.954150i
$903$	−1299.48	+	2250.77i	−0.0478893	+	0.0829467i
$904$	−14316.4			−0.526720
$905$	60962.4			2.23918
$906$	6411.88	−	11105.7i	0.235122	−	0.407243i
$907$	−3605.66	−	6245.18i	−0.132000	−	0.228630i	0.792448	−	0.609940i	$-0.208806\pi$
$907$	−3605.66	−	6245.18i	−0.132000	−	0.228630i	−0.924447	+	0.381310i	$0.875473\pi$
$908$	6959.44	−	12054.1i	0.254358	−	0.440561i
$909$	10381.0	+	17980.3i	0.378784	+	0.656073i
$910$	11708.6	+	20279.9i	0.426524	+	0.738761i
$911$	29098.8			1.05827			0.529136	−	0.848537i	$-0.322516\pi$
$911$	29098.8			1.05827			0.529136	+	0.848537i	$0.322516\pi$
$912$	1732.59	+	1566.27i	0.0629078	+	0.0568689i
$913$	16040.7			0.581456
$914$	7040.20	+	12194.0i	0.254780	+	0.441292i
$915$	5633.02	+	9756.68i	0.203521	+	0.352509i
$916$	−7132.95	+	12354.6i	−0.257292	+	0.445643i
$917$	7985.71	+	13831.7i	0.287581	+	0.498104i
$918$	4163.64	−	7211.64i	0.149696	−	0.259281i
$919$	−15321.9			−0.549972			−0.274986	−	0.961448i	$-0.588673\pi$
$919$	−15321.9			−0.549972			−0.274986	+	0.961448i	$0.588673\pi$
$920$	−6177.11			−0.221362
$921$	506.804	−	877.811i	0.0181322	−	0.0314059i
$922$	7353.08	−	12735.9i	0.262647	−	0.454919i
$923$	22595.8			0.805796
$924$	−3841.32			−0.136764
$925$	28718.7	−	49742.2i	1.02083	−	1.76812i
$926$	14054.7	+	24343.5i	0.498777	+	0.863907i
$927$	−17819.2	+	30863.7i	−0.631346	+	1.09352i
$928$	−1062.78	−	1840.79i	−0.0375943	−	0.0651152i
$929$	10272.5	+	17792.4i	0.362787	+	0.628365i	0.988418	−	0.151754i	$-0.0484921\pi$
$929$	10272.5	+	17792.4i	0.362787	+	0.628365i	−0.625632	+	0.780118i	$0.715159\pi$
$930$	8203.45			0.289249
$931$	−4626.80	+	21556.9i	−0.162876	+	0.758861i
$932$	−23964.8			−0.842267
$933$	32.2936	+	55.9341i	0.00113317	+	0.00196270i
$934$	5875.16	+	10176.1i	0.205826	+	0.356501i
$935$	29883.6	−	51760.0i	1.04524	−	1.81041i
$936$	6166.59	+	10680.8i	0.215343	+	0.372985i
$937$	−23917.7	+	41426.6i	−0.833891	+	1.44434i	0.0610397	+	0.998135i	$0.480558\pi$
$937$	−23917.7	+	41426.6i	−0.833891	+	1.44434i	−0.894930	+	0.446206i	$0.852775\pi$
$938$	−691.469			−0.0240696
$939$	−8608.00			−0.299160
$940$	7780.39	−	13476.0i	0.269966	−	0.467595i
$941$	222.655	−	385.650i	0.00771344	−	0.0133601i	−0.862143	−	0.506665i	$-0.830878\pi$
$941$	222.655	−	385.650i	0.00771344	−	0.0133601i	0.869856	+	0.493305i	$0.164211\pi$
$942$	1592.57			0.0550835
$943$	8948.70			0.309024
$944$	−1487.90	+	2577.13i	−0.0513000	+	0.0888541i
$945$	−8139.12	−	14097.4i	−0.280175	−	0.485278i
$946$	−10463.0	+	18122.4i	−0.359598	+	0.622842i
$947$	−22023.0	−	38145.0i	−0.755705	−	1.30892i	−0.945023	−	0.327004i	$-0.893961\pi$
$947$	−22023.0	−	38145.0i	−0.755705	−	1.30892i	0.189318	−	0.981916i	$-0.439372\pi$
$948$	4147.50	+	7183.69i	0.142094	+	0.246113i
$949$	619.775			0.0211999
$950$	−10562.5	+	49212.1i	−0.360728	+	1.68068i
$951$	−10341.6			−0.352629
$952$	−1626.88	−	2817.83i	−0.0553859	−	0.0959313i
$953$	−1758.66	−	3046.10i	−0.0597783	−	0.103539i	0.834588	−	0.550875i	$-0.185706\pi$
$953$	−1758.66	−	3046.10i	−0.0597783	−	0.103539i	−0.894366	+	0.447336i	$0.852373\pi$
$954$	2701.30	−	4678.79i	0.0916750	−	0.158786i
$955$	−7251.95	−	12560.7i	−0.245725	−	0.425609i
$956$	1212.96	−	2100.90i	0.0410354	−	0.0710753i
$957$	7279.66			0.245891
$958$	355.562			0.0119913
$959$	−2895.87	+	5015.80i	−0.0975105	+	0.168893i
$960$	1168.06	−	2023.14i	0.0392697	−	0.0680171i
$961$	−17163.9			−0.576144
$962$	−24391.7			−0.817484
$963$	−19236.2	+	33318.1i	−0.643696	+	1.11491i
$964$	6890.34	+	11934.4i	0.230210	+	0.398736i
$965$	−620.257	+	1074.32i	−0.0206910	+	0.0358378i
$966$	−575.856	−	997.413i	−0.0191800	−	0.0332207i
$967$	7621.77	+	13201.3i	0.253464	+	0.439012i	0.964477	−	0.264166i	$-0.0850967\pi$
$967$	7621.77	+	13201.3i	0.253464	+	0.439012i	−0.711013	+	0.703179i	$0.751763\pi$
$968$	−20280.9			−0.673401
$969$	−5026.20	−	4543.70i	−0.166630	−	0.150634i
$970$	49568.5			1.64077
$971$	−1633.51	−	2829.33i	−0.0539876	−	0.0935092i	0.837769	−	0.546025i	$-0.183860\pi$
$971$	−1633.51	−	2829.33i	−0.0539876	−	0.0935092i	−0.891756	+	0.452516i	$0.850526\pi$
$972$	−6560.80	−	11363.6i	−0.216500	−	0.374988i
$973$	5458.87	−	9455.05i	0.179860	−	0.311526i
$974$	12319.9	+	21338.7i	0.405293	+	0.701989i
$975$	17279.1	−	29928.2i	0.567562	−	0.983047i
$976$	4938.29			0.161958
$977$	40038.2			1.31109			0.655545	−	0.755156i	$-0.272439\pi$
$977$	40038.2			1.31109			0.655545	+	0.755156i	$0.272439\pi$
$978$	380.068	−	658.298i	0.0124266	−	0.0215236i
$979$	−4158.11	+	7202.06i	−0.135744	+	0.235116i
$980$	22052.6			0.718821
$981$	1219.09			0.0396763
$982$	−8441.83	+	14621.7i	−0.274328	+	0.475149i
$983$	−11127.2	−	19272.9i	−0.361040	−	0.625340i	0.627092	−	0.778945i	$-0.284245\pi$
$983$	−11127.2	−	19272.9i	−0.361040	−	0.625340i	−0.988132	+	0.153605i	$0.950912\pi$
$984$	−1692.15	+	2930.89i	−0.0548210	+	0.0949527i
$985$	−3876.58	−	6714.43i	−0.125399	−	0.217197i
$986$	3083.09	+	5340.07i	0.0995797	+	0.172477i
$987$	2901.28			0.0935652
$988$	20341.6	−	6564.78i	0.655012	−	0.211390i
$989$	−6274.06			−0.201722
$990$	−30766.4	−	53289.0i	−0.987698	−	1.71074i
$991$	−7389.74	−	12799.4i	−0.236875	−	0.410279i	0.722941	−	0.690910i	$-0.242790\pi$
$991$	−7389.74	−	12799.4i	−0.236875	−	0.410279i	−0.959816	+	0.280630i	$0.909456\pi$
$992$	1797.93	−	3114.10i	0.0575446	−	0.0996701i
$993$	7813.60	+	13533.6i	0.249705	+	0.432502i
$994$	−3068.68	+	5315.10i	−0.0979200	+	0.169602i
$995$	−95340.5			−3.03768
$996$	−1818.85			−0.0578638
$997$	−14444.2	+	25018.1i	−0.458829	+	0.794716i	−0.998899	−	0.0469043i	$-0.985064\pi$
$997$	−14444.2	+	25018.1i	−0.458829	+	0.794716i	0.540070	+	0.841620i	$0.318398\pi$
$998$	−6211.24	+	10758.2i	−0.197007	+	0.341227i
$999$	16955.6			0.536990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.c.c.7.2	✓	6
3.2	odd	2		342.4.g.f.235.1		6
4.3	odd	2		304.4.i.e.273.2		6
19.7	even	3		722.4.a.j.1.2		3
19.11	even	3	inner	38.4.c.c.11.2	yes	6
19.12	odd	6		722.4.a.k.1.2		3
57.11	odd	6		342.4.g.f.163.1		6
76.11	odd	6		304.4.i.e.49.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.2	✓	6	1.1	even	1	trivial
38.4.c.c.11.2	yes	6	19.11	even	3	inner
304.4.i.e.49.2		6	76.11	odd	6
304.4.i.e.273.2		6	4.3	odd	2
342.4.g.f.163.1		6	57.11	odd	6
342.4.g.f.235.1		6	3.2	odd	2
722.4.a.j.1.2		3	19.7	even	3
722.4.a.k.1.2		3	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-0.881294 - 1.52645i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(10.3546 + 17.9347i) q^{5} +(1.76259 - 3.05289i) q^{6} +8.76259 q^{7} -8.00000 q^{8} +(11.9466 - 20.6922i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-0.881294 - 1.52645i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(10.3546 + 17.9347i) q^{5} +(1.76259 - 3.05289i) q^{6} +8.76259 q^{7} -8.00000 q^{8} +(11.9466 - 20.6922i) q^{9} +(-20.7092 + 35.8694i) q^{10} -62.1780 q^{11} +7.05035 q^{12} +(32.2611 - 55.8778i) q^{13} +(8.76259 + 15.1772i) q^{14} +(18.2509 - 31.6115i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(23.2077 + 40.1970i) q^{17} +47.7866 q^{18} +(17.3798 - 80.9750i) q^{19} -82.8369 q^{20} +(-7.72241 - 13.3756i) q^{21} +(-62.1780 - 107.696i) q^{22} +(18.6424 - 32.2895i) q^{23} +(7.05035 + 12.2116i) q^{24} +(-151.936 + 263.161i) q^{25} +129.044 q^{26} -89.7038 q^{27} +(-17.5252 + 30.3545i) q^{28} +(33.2119 - 57.5247i) q^{29} +73.0036 q^{30} +112.370 q^{31} +(16.0000 - 27.7128i) q^{32} +(54.7971 + 94.9114i) q^{33} +(-46.4155 + 80.3939i) q^{34} +(90.7332 + 157.155i) q^{35} +(47.7866 + 82.7688i) q^{36} -189.018 q^{37} +(157.633 - 50.8723i) q^{38} -113.726 q^{39} +(-82.8369 - 143.478i) q^{40} +(120.005 + 207.854i) q^{41} +(15.4448 - 26.7512i) q^{42} +(-84.1370 - 145.730i) q^{43} +(124.356 - 215.391i) q^{44} +494.812 q^{45} +74.5695 q^{46} +(-93.9241 + 162.681i) q^{47} +(-14.1007 + 24.4231i) q^{48} -266.217 q^{49} -607.744 q^{50} +(40.9056 - 70.8506i) q^{51} +(129.044 + 223.511i) q^{52} +(56.5285 - 97.9102i) q^{53} +(-89.7038 - 155.372i) q^{54} +(-643.830 - 1115.15i) q^{55} -70.1007 q^{56} +(-138.921 + 44.8334i) q^{57} +132.848 q^{58} +(-92.9940 - 161.070i) q^{59} +(73.0036 + 126.446i) q^{60} +(-154.322 + 267.293i) q^{61} +(112.370 + 194.631i) q^{62} +(104.684 - 181.317i) q^{63} +64.0000 q^{64} +1336.20 q^{65} +(-109.594 + 189.823i) q^{66} +(-19.7279 + 34.1697i) q^{67} -185.662 q^{68} -65.7176 q^{69} +(-181.466 + 314.309i) q^{70} +(175.101 + 303.284i) q^{71} +(-95.5731 + 165.538i) q^{72} +(4.80280 + 8.31870i) q^{73} +(-189.018 - 327.389i) q^{74} +535.601 q^{75} +(245.746 + 222.155i) q^{76} -544.840 q^{77} +(-113.726 - 196.979i) q^{78} +(588.269 + 1018.91i) q^{79} +(165.674 - 286.956i) q^{80} +(-243.504 - 421.761i) q^{81} +(-240.010 + 415.709i) q^{82} -257.980 q^{83} +61.7793 q^{84} +(-480.614 + 832.448i) q^{85} +(168.274 - 291.459i) q^{86} -117.078 q^{87} +497.424 q^{88} +(66.8743 - 115.830i) q^{89} +(494.812 + 857.039i) q^{90} +(282.691 - 489.634i) q^{91} +(74.5695 + 129.158i) q^{92} +(-99.0313 - 171.527i) q^{93} -375.696 q^{94} +(1632.22 - 526.763i) q^{95} -56.4028 q^{96} +(-598.387 - 1036.44i) q^{97} +(-266.217 - 461.101i) q^{98} +(-742.819 + 1286.60i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9	\( 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9} + 2 q^{10} + 8 q^{11} + 40 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} - 48 q^{16} - 51 q^{17} - 216 q^{18} + 40 q^{19} + 8 q^{20} - 170 q^{21} + 8 q^{22} + 47 q^{23} + 40 q^{24} - 338 q^{25} + 516 q^{26} + 718 q^{27} - 104 q^{28} - 125 q^{29} - 308 q^{30} - 100 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} - 84 q^{35} - 216 q^{36} - 376 q^{37} + 322 q^{38} - 1546 q^{39} + 8 q^{40} + 475 q^{41} + 340 q^{42} - 73 q^{43} - 16 q^{44} + 3188 q^{45} + 188 q^{46} - 241 q^{47} - 80 q^{48} - 1354 q^{49} - 1352 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} + 718 q^{54} - 1838 q^{55} - 416 q^{56} + 1755 q^{57} - 500 q^{58} - 1065 q^{59} - 308 q^{60} - 981 q^{61} - 100 q^{62} - 872 q^{63} + 384 q^{64} + 586 q^{65} - 548 q^{66} + 877 q^{67} + 408 q^{68} - 1526 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} + 667 q^{73} - 376 q^{74} + 4584 q^{75} + 484 q^{76} - 492 q^{77} - 1546 q^{78} + 1671 q^{79} - 16 q^{80} - 1287 q^{81} - 950 q^{82} + 1176 q^{83} + 1360 q^{84} - 1929 q^{85} + 146 q^{86} - 6430 q^{87} - 64 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} + 188 q^{92} - 3138 q^{93} - 964 q^{94} + 4489 q^{95} - 320 q^{96} - 985 q^{97} - 1354 q^{98} - 3184 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9 + 2 * q^10 + 8 * q^11 + 40 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 - 48 * q^16 - 51 * q^17 - 216 * q^18 + 40 * q^19 + 8 * q^20 - 170 * q^21 + 8 * q^22 + 47 * q^23 + 40 * q^24 - 338 * q^25 + 516 * q^26 + 718 * q^27 - 104 * q^28 - 125 * q^29 - 308 * q^30 - 100 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 - 84 * q^35 - 216 * q^36 - 376 * q^37 + 322 * q^38 - 1546 * q^39 + 8 * q^40 + 475 * q^41 + 340 * q^42 - 73 * q^43 - 16 * q^44 + 3188 * q^45 + 188 * q^46 - 241 * q^47 - 80 * q^48 - 1354 * q^49 - 1352 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 + 718 * q^54 - 1838 * q^55 - 416 * q^56 + 1755 * q^57 - 500 * q^58 - 1065 * q^59 - 308 * q^60 - 981 * q^61 - 100 * q^62 - 872 * q^63 + 384 * q^64 + 586 * q^65 - 548 * q^66 + 877 * q^67 + 408 * q^68 - 1526 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 + 667 * q^73 - 376 * q^74 + 4584 * q^75 + 484 * q^76 - 492 * q^77 - 1546 * q^78 + 1671 * q^79 - 16 * q^80 - 1287 * q^81 - 950 * q^82 + 1176 * q^83 + 1360 * q^84 - 1929 * q^85 + 146 * q^86 - 6430 * q^87 - 64 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 + 188 * q^92 - 3138 * q^93 - 964 * q^94 + 4489 * q^95 - 320 * q^96 - 985 * q^97 - 1354 * q^98 - 3184 * q^99

Introduction

L-functions

Modular forms

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